There are parallel train tracks running from Abilene to Imogene. The tracks run in a straight line between the two cities. On a particular morning, Train A begins the journey from Abilene to Imogene on the first track. At the exact same time, Train B begins the journey from Imogene to Abilene on the second track. The two trains always travel at constant velocities.

The two trains pass each other at a small town called Xanadu. From there, Train A takes another 5 hours to reach Imogene, while Train B takes another 10 hours to reach Abilene.

The next day, Train A embarks on the return trip to Abilene at the exact same time Train B leaves for Imogene. This time, they pass each other at a small town called Yonkers, whereby Train A takes another 5 hours to reach Abilene while Train B takes another 10 hours to reach Imogene.

If the distance between Yonkers and Xanadu is 500 miles, then how fast is each train traveling?

(In reply to Solution by Bractals)

You can prove that |AY| = |XI|.

A-------------X------------------------------I

     500 - d                    d

Velocity of train A is distance/time or d/5.

 

A----------------------------Y---------------I

                  e                       500 - e

Velocity of train A on the way back is e/5.

 

Since they have constant velocities, d/5 = e/5.

Therefore, d=e, and |AY| = |XI|.

 

This might seem trivial, but what the hell.

 

Posted by Skizap on 2007-06-14 13:33:26