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### Car Laps

```
Date: 01/26/2001 at 14:11:46
From: Andy Chang
Subject: Distance and Rate

On a race track, one car travels five laps a minute and another car
travels eight laps a minute. How long will it be before the second car
laps the first?
```

```
Date: 01/26/2001 at 16:04:49
From: Doctor Greenie
Subject: Re: Distance and Rate

Hi, Andy -

You can answer this question using algebra, but it's almost easier in
this case to answer just by some careful analysis.

By using algebra:

In x minutes, the number of laps traveled by the first car is 5x, and
the number of laps traveled by the second car is 8x. We want to find
the value of x for which the second car has traveled one lap farther
than the first:

8x = 5x + 1

This is an elementary algebra equation that gives us the answer
x = 1/3 minute.

By using careful analysis:

The second car goes 8 laps a minute while the first car goes only five
laps in that same minute. The second car therefore goes three laps
farther every minute, so it laps the other car three times each
minute. So it laps the first car every 1/3 minute, and the first time
it laps the first car is after 1/3 of a minute, or 20 seconds.

- Doctor Greenie, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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