Math for Grownups (29 page)

There’s no rule in mathematics that says you need to be consistent with the units you use. Every time you solve a problem, you should choose the method that works best for you.

When Quinton was finding the amount of time he was going to be in a plane, he just left his units as hours and minutes. That’s because it’s pretty simple to add 5 hours to 45 minutes.

But when he got to the next step of his problem—adding the layover—he decided that switching things up a bit would help him out.

When Quinton thought of 5¾ hours as 5½ + ¼ hours, did that make sense to you? If not, try something different. Think of the numbers as decimals. Imagine a clock face. Or get really crazy and picture quarters and dollars. (A quarter is 25¢ or ¼ of a dollar or $0.25.)

Look, your methods don’t have to make sense for someone else. They just have to work for you.

Of course, they also need to be mathematically sound, but you might be surprised at how many different ways math can be done—and result in the correct answer.

When you’re traveling by car, determining your ETA can be a little tricky. That’s because there’s no pilot estimating the length of the trip for you.

You’ll also need to consider the speed limit, which depends on your route—interstate, curvy country roads, through the city with stop-and-go traffic, or a combination of these. A long stretch of highway isn’t the most exciting route to take, but it may be the fastest, simply because you’ll probably maintain a steady speed.

These days, your on-board GPS or a good online map can give you the info you need in an instant. But with different state speed limits and routes, you may want to do a little figuring on your own anyway.

Amanda is so exited! Her little sister is having a baby, and she’s going to be there for the birth. Mary Helen just called to tell her that she’s on her way to the hospital, so Amanda jumps in her car and hits the road.

In preparation for this moment, Amanda did some math last week, to be sure she knew how long it would take her to get there. Mary Helen recently moved to a new city, and Amanda hasn’t had a chance to visit yet. She’s not worried about getting lost—it’s pretty much a straight shot down the interstate—but she is worried about making it there on time.

Using a map, she figures out that it is 180 miles from her house to Mary Helen’s hospital. Now all she needs to do is find out how long the drive will take.

She’ll be driving from Ohio, where the speed limit is 65 mph, to West Virginia, where it’s 70 mph. Nearly all of her driving will be on interstates. How does she come up with her answer?

Amanda could have tallied the number of miles she’d be driving in each state, but when she looked at the map, she noticed that it’s just about half-and-half. That level of estimation works for her, so she decides on a plan of action: She’ll average the speed limits and then use that result to find how long she’ll be driving.

To average two numbers, just add them up and divide by 2. But Amanda’s been doing mental math for a long time, and she’s got a shortcut for a problem like this one. All she needs to do is find the midpoint of 65 and 70. In other words, she needs to know what number falls exactly between 65 and 70.

Turns out the average is 67.5 mph.

The key in the previous sentence isn’t 67.5; it’s
mph
, or miles per hour. That’s because:

Speed is measured in miles per hour

Speed
=
miles
/
hour

To make the math a little easier, let’s substitute some variables here (
r
for rate,
d
for distance, and
t
for time).

First, she substitutes for her variables.

To get the
t
by itself, she has to multiply each side of the equation by
t
.
(Multiplying the right-hand side of the equation by
t
gets rid of it.)

Now she can divide each side of the equation by 67.5 to isolate
t
.

Finally, she divides 180 by 67.5.

t
=
2.666 …

2.666 … is pretty close to 3 hours, and Amanda always needs at least one potty break, so she rounds up.

Unless Mary Helen’s labor is really, really short, Amanda should arrive in plenty of time.

Kathy loves her extended family. She really does. And she really enjoyed their weeklong vacation to the Outer Banks last summer.

Except for one thing: the bickering over money.

A beach vacation isn’t cheap, and when you split the costs among four very different-sized families, plus the matriarch, there are bound to be some hard feelings. Something has to be done, or Kathy’s not going this year.

She vows to come up with a plan that will make everyone happy.

First, she thinks about where the problems were last year. Her sister Florence, who has 1 child, and her sister Jocelyn, who came by herself, didn’t think it was fair that they paid as much as Kathy and their sister Dorothy did. That makes sense, actually, because Kathy has 4 kids and a husband, and Dorothy came with 3 kids and her husband.

Certainly Florence, her daughter, and Jocelyn didn’t eat as much as Kathy’s family did, and they didn’t take up as much room in the house.

Luckily, the house has plenty of space—eight bedrooms that sleep fifteen people in all. And the room assignments worked out pretty well. Each couple had a room with a double bed, Florence bunked with her daughter, and Jocelyn and Mom each had single rooms. The other seven kids shared the three remaining bedrooms.

Already, Kathy is getting confused, so she decides to make a chart to keep things in order.

Looking at her chart, Kathy has an idea. They’re all sharing space, although some families are taking up more room than others. The same goes for groceries. (Kathy figures each family can be responsible for its own entertainment and transportation costs.)