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t’s summer. It’s hot. I’m busy with 9 million things. And so today, I bring you an excerpt from my book, Math for Grownups. If you’re wondering how to figure out the best vacation deal for you, read through this example. A little bit of planning–and math!–can help you relax, while you’re saving some cash.

Going on vacation means packing, finding someone to take care of Fido, and taking some time off from work. It also means charging some pretty hefty items on your credit card.

The finances of vacationing can boggle the mind. And even with online trip planners and the ability to comparison-shop with the click of a mouse, planning a vacation can make you ready for another one.

Red and Emily are ready for their second honeymoon. After 25 years of marriage, two kids, and the stress of everyday life, they deserve it. So Red is going to surprise Emily on their anniversary with a 1-week getaway to Aruba.

For 5 years, he’s been secretly putting away a little cash here and there. He’s got $7,500 saved up, and that’s just enough to whisk his bride away for some R & R. (That’s romance and rest.) Red has even arranged for Emily to take some time off from work.
But first he’s got to figure out how he can spend his vacation nest egg. After Emily goes to sleep, he cruises trip-planning websites looking for the best deal. And he’s very quickly overwhelmed.

There are all-inclusive packages, non-inclusive packages, romance packages, and adventure packages. Some include the cost of flights and drinks and meals. Others offer some combination of these features.

It’s going to be a long night.

Within an hour or so, Red has some options scribbled down on a piece of paper. He has chosen their destination—a secluded resort with 5-star dining, access to a private beach, a spa, and great online reviews. Now it’s on to the pricing. There are a number of options:

Because two of his options don’t include airfare, Red prices out some flights. He finds out that he can get two round-trip tickets for about $925. Not bad!

If he chooses a non-inclusive option, he’ll need to pay for meals, drinks, and activities. And that requires more research. Red wonders whether there is a good way to estimate these.

He considers meals first. The resort includes a free breakfast, so he won’t need to include that in his calculations. But unless they’re going with the all-inclusive option, they will have to buy lunches and dinners. Red does some more research and comes up with the following numbers:

Average lunch → $25/person
Average dinner → $60/person
Average lunch → $25/person
Average dinner → $60/person

And because there are two of them, and they’ll be there for 7 full days:

Lunches: $50 per day for 7 days = $350
Dinners: $120 per day for 7 days = $840

It looks like the cost of meals will be $350 + $850, or $1,190.

He and Emily aren’t big drinkers, so that’s pretty simple to figure out. Assuming that the cost of drinks is pretty high, he guesses $25 a day for two fancy cocktails, and if they have a nice bottle of wine with dinner each night, that’ll run them about $200 for the week.

($25 • 7) + $200 = $375

Now, Red thinks about activities. A day on a sailboat and some snorkeling sounds great ($450). Then he’d like to book a few spa treatments for Emily ($500).

$450 + $500 = $950

Because all of the prices so far have included tax, Red doesn’t no need to do any math for that. But he will need to tip the baggage carriers, taxi drivers, servers, and spa staff. Red takes a shot in the dark, and guesses $350 for all gratuities. (That could be too much, but it’s probably not going to be too little.)

This is a ton of information, and Red’s legal pad looks like a football coach’s playbook. He’d better get organized if he wants to book this trip and get some sleep. Red decides to make a list.

Package

All-inclusive = $7,225

Romance package: $6,150 (package) + $925 (air) =  $7,075

Hotel + Travel: $4,340 (hotel/air) + $1,915 (meals/drinks/tips) + $950 (activities) =       $7,205

A la carte: $3,450 (hotel) + $925 (air) + $1,915 (meals, etc.) + $950 (activities) =  $7,240

Now Red can really consider his options.

The most expensive choice is à la carte, but all of the totals are pretty darned close. If he goes by price alone, the clear winner is the Hotel + Travel package. But that requires him to handle everything on his own—and honestly, he’s ready for bed.

On the other hand, the Romance package is only $70 more. And right now, that extra bit of cash seems worth it. Red pulls out his credit card and books their flights and vacation packages. Then he snuggles up next to Emily and savors his little surprise!

How have you found the best travel deals? Share your ideas in the comments section.

I’m no big world traveler. So when faced with the prospect of filling an entire month with travel-related blog posts, I reached out to more experienced folks. Fellow freelance writer, Beth Hughes offered to write this post, detailing how she’s able to hop the globe on a limited budget. While there’s not a lot of hard math here, she does share a really smart estimation tip that helps her keep cash in her wallet–for her next trip. And you can definitely see how a little bit of planning and observation adds up to big savings. So, welcome Beth!

When I travel, I usually head to pricey places like Japan, Hong Kong and Hawaii. Yet I’ve figured out how to make these trips without breaking the bank, even when the dollar is weak. The key is planning, observing, and a little mental trickery.

Before you go

Use a travel agent. Because I usually travel with a friend, my agent, Julie Sturgeon of Curing Cold Feet, creates custom group packages for us. Savings on our last 10-day jaunt to Hawaii were about $20 each, or a tank of gas. Some years, she saves us twice that.   Savings: $20-$40

Decide how connected you must be. Free WiFi is not ubiquitous. Select a hotel with free WiFi so you can stay in touch via email and Skype if you have a smartphone or other device.  Savings: up to $20 per day

Make sure you select a hotel that equips the rooms with an electric kettle and a refrigerator. Pack food for your arrival if you’re getting in late–small cans of pop-top tuna, packs of instant oatmeal, a little jar of peanut butter and some crackers. Pack coffee or tea, and any equipment for preparing it. Savings: about $10 per day

Research the fees your bank’s ATM network, what it charges for ATM withdrawals and what service fee it tacks onto credit card purchases outside the United States. Your goal is to reduce the fee burden by withdrawing enough cash from an affiliated ATM to cover anticipated expenses for five or six days. You get a better exchange rate than you do at a moneychanger. In Tokyo recently, the airport moneychanger offered ¥71 for each US$1 while an affiliated bank’s ATM gave me ¥78. Stash the extra cash in your hotel room safe. Avoid using your credit card for a cash advance. The interest rates are punishing. Savingsup to $25

Upon Arrival

Buy a SIM card with the least expensive international call and data plan that you can top off online using a credit card. (In Japan, tourists must rent SIM cards.) The SIM card will be valid for as long as six months. You will probably leave money behind but compared with international roaming charges, it’s less than a pittance. Savings: up to $50

After a good night’s sleep,  start saving by making breakfast in your room. While this is a traveler’s tip as old as the Appian Way I figure it saved us about $200 each on a recent Tokyo stay.

Here’s how: Our budget hotel offered a daily breakfast buffet for ¥1,900 per person, or a whopping $208 per person if we had indulged for all nine mornings of our stay. So we traveled with a pound of ground coffee, which cost US$12, filters, a drip cone and our own tall, insulated travel mugs. That gave us each two cups of good coffee each morning with plenty left over for a boost if we returned in the afternoon before setting out on the night shift. We stocked up on individual yogurts, which averaged ¥100 each, spent about the same amount on fresh fruit and bought a pint of milk for coffee.

Our breakfast total per person for nine days: about ¥2,000, or $25. We’re not big breakfast eaters but if we could have added in bags of granola (¥298 per) or boxes of cereal (¥350- ¥500) and still saved. Savings: $200

Our trick for lunch in an expensive city is “Follow the office ladies!” They gravitate to good, cheap food. In Bangkok, I ended up in a utility company cafeteria that welcomed anybody who could find it, just by trailing office workers. On weekends, follow the middle-aged ladies traveling in pairs for a meal out with good chat on the side. Rarely did lunch in Tokyo cost more than $10 or $12. Wherever we ended up, and it was never a food court, we would order one of the lunch specials, always and everywhere the cheap date of meals. By making lunch the main meal of the day, we were then free to indulge ourselves with happy hours or splash out with a dainty dinner at a big-name joint. Savings: $200

Mind Trick

Now for my mind game, and yes, I am dim enough to trick myself by rounding down when making mental currency conversions(Editor’s note: I don’t think this is dim at all–but a pretty darned smart use of estimations!)

Here’s how it worked on a trip to Hong Kong, where the exchange rate has been stable for the past 10 years: US$1 converting in a narrow range to HK$7.8 to HK$7.6.

Rather than deal with decimals, I divided a price in HK dollars by US$7. This made everything from menu selections to a pink leather wallet that caught my eye seem more expensive than they were. So much for splurging in a notorious paradise for food and fashion.

I also set a daily budget. If I came in under, I didn’t automatically roll the money over to the next day. I put it in a separate pocket in my wallet. Then, when a local friend suggested a Michelin-starred restaurant for lunch, I ponied up from my secret stash.

Even with that magnificent meal, I returned home with US$279 of my budgeted travel kitty unspent. That’s a whisker less than half the cost of a ticket from the West Coast to Hawaii, and about one quarter the price of my next trans-Pacific flight. I’m thinking late November, early December before the holiday rush when the fares spike.

Do you have questions for master traveler Beth Hughes? If so, please ask in the comments section. And share your own cash-saving tips for travel!

Earlier this month, I showed you how to convert currencies, when given the exchange rate. When you’re not using an online calculator, that process involves proportions, which are pretty simple to use, but do require a little figuring on paper. This same process works for any conversions, including miles to kilometers, liters to ounces, etc.

But while being exact with your money is pretty important, estimating how far you have to drive or walk is usually good enough. So instead of going into details about metric-to-traditional measurement conversions, let’s look at how you can find these distances with a little mental math. First, you’ll need to know a few facts:

1. A mile is longer than a kilometer. So, when you convert miles to kilometers, the answer  will be larger than the original amount. (mi –> km = larger answer)

2. A kilometer is shorter than a mile. So, when you convert kilometers to miles, the answer will be smaller than the original amount (km –> mi = smaller answer)

2. In fact, 1 mile equals 1.61 kilometers. And 1 kilometer equals 0.625 mile.

3. Those values are pretty darned close to 1.5 kilometers and 0.5 mile.

Remember, we’re estimating here, so you’re not looking for an exact answer. Forget what your middle school math teacher said about the precision of math. You don’t always need to getan exact answer. But there’s another fact you’ll need to consider:

4. The larger the value that you’re converting, the less precise your answer will be.

If you depend on the estimate 1 mi = 1.5 km and you’re converting 15 mi to km, your answer will be pretty close. BUT if you’re converting 1,468 mi to km, your estimate will be a lot lower than the actual answer.

Look, estimating is no big deal. In fact it’s a really, really powerful tool that can make your life much easier. You do need to know when estimation is in your best interests and when you should pull out the calculator. (See? Math really isn’t all that black and white!)

Let’s look at an example. Zoe has finally made it to London! She’s spending the summer studying Shakespeare and working part-time as a docent at the Tate Modern. And she’ll have some time to roam around Europe a bit. She’s rented a car so that she can chart her own path, and next Friday afternoon, she’s going to cross the channel to France, where she hopes to spend four days winding her way down to Paris and back.

But how long will it take her to get there? According to her map, the distance is 454 km. Since Zoe is used to miles, she’d like to convert the distance so that it makes more sense to her. She’s okay with a rough estimate, especially since she has no firm schedule. So she decides that knowing there are about 1.5 km in a mile is good enough.

To make the math even easier, she decides to round the distance as well: 450 is pretty close to 454. Now she can easily do the math in her head, but we’ll get to that in a minute. Let’s write it out first.

Because she’s converting kilometers (shorter) to miles (longer), her answer will be smaller than the original amount. That means she’ll need to divide.

450 km ÷ 1.5 = 300 mi

So she’ll travel about 300 miles to get from London to Paris — not a huge distance!

But how could she do this in her head? For that, she’ll need to remember a few things about fractions.

1.5 = 3/2

450 ÷ 1.5 = 450 ÷ 3/2

450 ÷ 3/2 = 450 • 2/3

(That’s because when you divide by a fraction, it’s the same thing as multiplying by its reciprocal — or the same fraction upside down.)

So in order to convert kilometers to miles in her head, she’ll need to multiply the value by 2 and then divide by 3 (which is the same as multiplying the value by 2/3. In other words:

450 • 2/3 = (450 • 2) ÷ 3 = 900 ÷ 3 = 300

Whew!

But once Zoe remembers this little trick, she can estimate these conversions quickly and easily.

30 km = ? mi

30 km • 2 = 60

60 ÷ 3 = 20

30 km = 20 mi (approximately)

Make sense? Try it for yourself: convert 75 km to mi and then use an online calculator to check your answer. Remember, if you’re using the process above, you’ll get an estimate, not an exact value!

So take a guess: If you’re converting mi to km, what process would you use? See if you can figure it out and then offer your explanation in the comments section. Feel free to choose a value to convert, if it’s easier to explain that way.

I’m vacationing this week in sunny Radford, Virginia,and ike most parts of the United States, the metric system is not used here (to mark distances, anyway). But if you cross the border into another part of the world, there’s little doubt that you’ll be measuring kilometers rather than miles and grams instead of pounds. That’s because most of the world has embraced the metric system. (In fact, only two other countries — Burma and Liberia — have resisted the change along with the U.S.)

Ask any scientist or mathematician: the metric system is infinitely more intuitive and much, much easier to remember and understand. But why? The answer is simple: Base 10. What this means is even simpler: in base 10 the foundational number is 10. Take a look:

10 • 1 = 10

10 • 10 = 100

10 • 100 = 1,000

and so on…

Each time you add a digit in our number system, you are effectively multiplying by 10. That means that 99 is the last two-digit number in base ten, and 999 is the last three-digit number. In fact our entire decimal system is base ten. (But it wasn’t always like that.)

But here’s the thing — you don’t care (and you shouldn’t really care). We are so used to base 10 that we don’t even think about it any more. It’s like knowing how to ride a bicycle or drive a car; once you learn it, you don’t even give it a second thought, but if you’re asked about it, it’s hard (or impossible) to explain.

When you were in school, you probably were asked to convert numbers into different base systems — and this was probably pretty darned confusing. We’re not going to do that here for one simple reason: You don’t need to know how to do this. BUT it is important to know that different base systems are useful in a variety of situations and professions. For example, computers function in base 2 (or binary), which is simply a system of zeros and ones. Computer graphics depend on a hexadecimal system or base 16 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F). Crazy, huh? Even less technical situations depend on a variety of bases — dozens and grosses are base 12 (one dozen is 1 • 12 and one gross is 12 • 12).

Compared to these other bases, base 10 is pretty darned easy, right? And that’s why so many mathy folks don’t understand why our country hasn’t embraced the metric system. Yep, unlike traditional measure systems, the metric system is base ten. Let’s compare:

Traditional system: 12 inches = 1 foot

Metric system: 100 centimeters = 1 meter

Traditional system: 5,280 feet = 1 mile

Metric system: 1,000 meters = 1 kilometers

Just a glance at these conversions and even the most math-phobic person would probably agree: the metric system is much easier to maneuver.

But agreeing that the metric system is easier doesn’t help you with conversions when you’re traveling, does it? On Wednesday, we’ll take a look at those conversions. I’ll show you some really easy ways to estimate the conversions. Because who wants to do math on vacation?

What other bases can you think of? How do you use them in your everyday life? Share your ideas in the comments section.

The details involved in a big vacation can be so overwhelming. And from determining the best prices on airfare to figuring out when you’re going to arrive at your destination, there’s a ton of math involved. That’s exactly why my family contacted Julie Sturgeon, owner of Curing Cold Feet, to help us plan our trip to the Galapagos Islands several years ago. Julie is just the person you want — detail oriented, always on the lookout for the best deal and very, very careful with your hard-earned cash. She proclaims a distinct fear of math, but she’s managed to turn that around and build a very successful travel agency. She was also kind enough to bare her math soul today.

Can you explain what you do for a living? I research, recommend, and book travel packages for both family vacations and business trips. This involves checking everything from airline schedules and prices to comparing amenities for the price at all-inclusive resorts, cruise lines, and hosted tour packages. I also book hotel rooms and car rentals.

When do you use basic math in your job?  Most of my math involves basic adding, subtracting and determining percentages. For instance, if a family wants to go to Walt Disney World for 5 days, but they know nothing more than that, I would prepare charts that show the costs of a value hotel with Hopper passes versus a moderate hotel with Hopper passes versus a deluxe hotel without Hopper passes. The chart would also show what happens to the price if you add any of the three meal plans to this vacation package. This way, families can weigh their values against their budget — at $3,200, for example, would they really need a sit-down meal every day versus a fast food option at their original budget of $2,400? Or should they keep the higher food plan and stay at a less expensive hotel?

Other times, I need to show vacationers why one package is better than another. For instance, a property may be running national commercials on all the cable channels advertising “30% off your stay in July.”  A couple wants to take advantage of that deal and calls asking for it specifically. Meanwhile, a supplier has a bulk inventory pricing on the property next door, which actually has higher ratings at Trip Advisor, and that total price comes out $100 less. And the property down the beach always offers rooms at the rate from the nationally advertised brand. I need to be able to explain in simple numbers why the 30% off deal isn’t really a sale in this circumstance, so they aren’t overly impressed with something that is, in fact, ordinary.

The second way I use math is more behind the scenes. Vacation packages require a deposit, with a final payment on a specified date. Just making sure you don’t over- or underpay requires a calculator. And sometimes it can become even more complicated when two people are sharing a room and want to divide the cost into two equal payments across two credit cards. I really have to stay on the numbers ball if they choose to make incremental payments before the final payment on split credit cards!

Do you use any technology to help with this math? I use a calculator as an insurance policy that the numbers come out right. Whenever I need to translate foreign currency quotes to US dollars, I use xe.com, and I use worldtimeserver.com when determining the time difference between two countries.

How do you think math helps you do your job better? It allows me to be an advisor and research assistant as opposed to a salesperson. I am more comfortable — and therefore more effective — in that role.

How comfortable with math do you feel? I am very math phobic. When I was a journalist, I had my engineering husband check any statistics conclusions I had to make, because I didn’t trust myself to choose the right formula to get the right answer. We have a pool table, and everyone in my family tells me the key to winning a game is to use geometric principles. I’ve never won a game. At one point in my life, I thought about getting an MBA but learned I’d need to take the GMAT for my admission application. So I decided to take math lessons, borrowed a seventh grader’s textbook and ended up in tears because I couldn’t understand it. Needless to say, I’ve never taken the GMAT, and I consider an MBA closed to me.

But this feels completely different because it’s about someone’s money. This counting makes sense to me, it feels important, and it really doesn’t stray that far from the basics I learned in grade school.

What kind of math did you take in high school? I was required to take two years of math to graduate, and I enrolled in algebra and geometry. I was allowed to take classes with the word “remedial” in them for the diploma, but my pride wouldn’t let me, since I was in the accelerated track for every other topic. I passed both math classes with a C, although I had to have a tutor to get me to that point, and I spent every in-class study period getting one-on-one help from the math teacher.

Did you have to learn new skills in order to do the math you use in your job? I had everything I needed except confidence. That came only when my desire to protect people’s hard-earned money was greater than my fear.

All you need to get comfortable with basic math is a victory. It gets easier from there. Start with balancing your checkbook. Or figuring out how much faster you will be out of debt if you pay X amount more each month on a financial commitment. The fact that it’s worth real money to you is a powerful motivation, and when you get it right, you know you can do it again.

Questions for Julie? Post them in the comments section, and I’ll be sure to let her know they’re here!

You’ve booked that trip to ParisVive les vacances! Now that your credit card has borne the brunt of your plane tickets and hotel reservations, with just enough space for a couple of fantastic meals, it’s time to turn to the cash. How much should you bring — and even more importantly, how far will it go?

When traveling out of country, you need to consider the currency exchange rate. Only very rarely is this exchange equal. (In other words, one Euro almost never equals one U.S. dollar.) That means, you’ll need to use a conversion to find out how far your cash will actually go.

There are actually three things to talk about here: using an online conversion calculator, doing the conversions by hand and checking your answer to see if it’s reasonable. Remember, math is infinitely flexible, so there’s no reason you have to do this in one particular way. Next Wednesday, we’ll look at doing conversions with paper and pencil. Today, it’s all about online calculators and checking your answer.

First, the conversion calculators. Go ahead and use them! If nothing else, a reliable online calculator will give you the most up-to-date conversion rate with the click of a button. For example, using the XE currency conversion calculator, I found that $1USD is equal to 0.794921€ (as of Monday, July 2, 2:05 p.m.).  This means that one U.S. dollar is worth a little more than 75 percent of a Euro.

If you know the exchange rate, it’s really easy to exchange values of 10, 100 or 1000. In these cases, you can simply move the decimal point.

$10USD = 7.94921€

$100USD = 79.4921€

$1000USD = 794.921€

Notice that when there is one zero (as in 10), you move the decimal point one place to the right. When there are two zeros (as in 100), you move the decimal point two places to the right. And when there are three zeros (as in 1000), you move the decimal point three places to the right.

Of course, if you want to convert $237.50USD to Euros, that trick won’t work. In that case, you can plug $237.50 into the online calculator. If you have $237.50USD in your pocket, that’s 188.717€.

XE also has iPhone and Droid apps, so you can take the online calculator on the road with you. (Note: I don’t have any relationship with XE. It just looks like a good, reliable online currency calculator. Want to recommend something different? Feel free to respond in the comments section.)

The thing about online calculators is that they’re only as good as the information that you put in. If you think you’re converting $USD to €, but you’re actually doing it the other way around, well, your fancy pants calculator is not going to spit out the answer you were looking for. You have to know how to assess whether your answer is correct.

I’m the first to admit that I get this very confused. I have to stop and think really hard to be sure that I’ve done the conversions correctly. (And to be honest, this is one of the reasons I prefer to do it by hand.) But there are some simple rules you can consider that will help:

  • If the conversion rate is less than 1, the conversion will be less than the original amount.
  • If the conversion rate is greater than 1, the conversion will be greater than the original amount.

Let’s say that $1USD equals $1.26SGD (Singapore dollar). If you convert $USD to $SGD, will your answer be greater or less than the original amount? If you said greater — you’re right! But if you convert $SGD to $USD, the answer will be less than the original amount. Make sense?

The good news is that you can figure this out before you leave. Write it down or keep a note on your phone. Then you will always be able to check to see if your answer makes sense. Because the worst thing is to come home from a relaxing vacation to find that you’ve spent way too much.

Be sure to come back next Wednesday to get the deets on how to do these conversions by hand. It really isn’t that difficult — and the process is applicable in so many other situations, so it’s worth learning.

Where are you traveling this summer? Share your plans in the comments section below!

Welcome to July! School is officially out, and temperatures have risen. This is the month when many folks decide to hit the road.

Whether you’re RVing across country, boarding a plane for a distant land or just heading down to the beach for some R&R, you’ll need to pack some math skills. From budgeting your costs to figuring out exactly when you’ll arrive, a vacation is no time to rest your brain cells completely. Math can help you save some cash, stay on time and even avoid a nasty sunburn.

This month, we’ll look at all of the ins and outs of travel math. We’ll hear from travel agents and other pros who play a role in your vacation plans. I’ll share some ways that math can keep you on track. Heck, we can even take a look at your odds in Vegas. (I promise, no trains leaving from two different stations at the same time — unless you need to that a problem like that solved for you.)

If you have ideas for a post, do drop me a line. In the meantime, I’ll leave you with this logic problem:

Three friends are traveling to their high school reunion together. They arrive at their hotel late at night, only to find that their reservations were lost.  There is only one room with three beds available. They have no choice but to share the room, which the hotel has discounted to $30. Each of them takes out a 10 dollar bill, which the clerk collects.

After the friends are settled into their room, the manager reconsiders the discount. (He feels terrible!) He decides to offer the room at only $25 and sends a porter upstairs with $5 for the three friends.

The porter starts thinking about how to divide the $5 into three equal parts. When he can’t figure it out, he decides to give $1 to each friend, and pocket the rest. The friends accept the $3 refund, and the porter heads back to his post, with the remaining $2.

Given their $3 refund, each of the three friends paid $9 for the room (3 • 9 = $27). The porter has $2 in his pocket, making the total $29 ($27 + $2 = $29). But the friends originally paid $30!

What happened to the $1?

Think you know the answer? Share it in the comments section. Then come back on Wednesday to see if you’re right!

Where is the $1? Post your answer in the comments section. Also, feel free to share your vacation math questions. I’ll address as many as I can throughout the month of July!

My daughter just bought a hot-pink slap watch. She thinks it’s cool because it’s a slap watch, that’s pink–with tiny Diamonique stones encircling the face.

I think it’s cool because it’s not digital.

Like most middle school kids, my daughter is not so good at reading an analog clock. In fact she resists it like crazy. But today, as I sit in the Philadelphia airport waiting for my 5:55 pm flight to Seattle, I’m thinking about how useful her new watch will be.

Read the rest of my guest post at www.TravelSavvyMom.com.  Then share your opinions on digital vs. analog clocks. Which one helps you calculate time fastest?