Average Speed

Date: 04/29/2001 at 20:26:48
From: Max Behringer
Subject: Algebra Word Problems

My teacher gave us this extra credit problem on a test:

A test track is 1 mile around. A driver drives 1 lap at 160 mph. How 
fast must he drive the second lap in order to average 200 mph for the 
two laps?

Everyone in my class thought it was 240 mph, but our teacher said that 
the problem was more complicated. He said we should break it apart.

Please help.

Date: 04/29/2001 at 21:31:38
From: Doctor Jaffee
Subject: Re: Algebra Word Problems

Hi Max,

I'll give you a different example and then you try to figure out the 
problem your teacher gave you.

Suppose a person drives somewhere at a rate of 20 mph, but returns at 
a rate of 60 mph. It would seem natural, then, to say that the average 
speed for the entire round-trip was 40 mph, but that would be wrong. 
I'll explain why. Let's assume that the one-way distance is 4 miles.

You know that the relation between d (the distance traveled), r (the 
rate of speed), and t (the time traveled) is d = r * t.

Going one way d = 4, r = 20, so if d = rt, then 4 = 20t and 
t = 1/5 hour = 12 minutes.

Returning, d = 4, r = 60, then 4 = 60t and t = 1/15 hour = 4 minutes.

So, the round trip was 8 miles in 16 minutes (16/60 = 4/15 hour). 
Therefore, if d = 8 and t = 4/15, then 8 = (4/15)r and r = 30.

The average speed was actually 30 miles per hour.

See if you can figure out the speed required during the second lap so 
that the average speed of the car over the two laps will be 200 miles 
per hour.

If you have a chance, write back and let me know what you found. Good 
luck.

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/