Passing Cyclists

Date: 08/31/2003 at 00:33:43
From: Sami
Subject: time

Two cyclists started to ride at 7am: one from A to B, the other from 
B to A. Each of them rode at a constant speed along the same road and 
when each arrived at the terminal point, immediately turned back. 
After they met for the 1st time, each of them turned exactly once 
before they met for the 2nd time at 6pm. Find the time of their 1st 
meeting.

Date: 08/31/2003 at 20:36:53
From: Doctor Greenie
Subject: Re: time

Hi, Sami--

Let C be the point where the two cyclists meet the second time.  Let 
the distance AC be x and the distance BC be y.

The two cyclists cycle for 11 hours (7am until 6pm) before meeting 
the second time.  In that time, the cyclist who started from A has 
traveled from A to C, from C to B, and from B to C, a total distance 
of (x+2y).  In the same time, the cyclist who started from B has 
traveled from B to C, from C to A, and from A to C, a total distance 
of (2x+y).

You now know the time each cyclist traveled and the distance each 
one traveled, so you can determine expressions for the rate for each 
cyclist.

You can also determine the total distance (in terms of x and y) the 
two cyclists needed to travel before meeting the first time.

And now you know how far the two cyclists together had to travel 
before meeting the first time; and you know the rate of each 
cyclist--so you can determine the amount of time they had to 
travel before meeting that first time....

I hope this helps. Please write back if you have any further 
questions about any of this.

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