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/