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Two Trains (Posted on 2007-05-05) Difficulty: 3 of 5
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?

No Solution Yet Submitted by hoodat    
Rating: 4.2500 (4 votes)

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Solution Solution | Comment 2 of 4 |

    A : Abilene
    I : Imogene 
    X : Xanadu
    Y : Yonkers
    t : Time to reach X = Time to reach Y
 v(A) : Velocity of train A
 v(B) : Velocity of train B

   |AX| = t*v(A) = 10*v(B)
   |XI| = t*v(B) = 5*v(A)
Solving these gives
   v(A) = v(B)*sqrt(2)
   t = 5*sqrt(2)
Since the description of the trips is the same,
we must conclude that |AY| = |XI|.
   |AX| = |AY| + |YX| = |XI| + |YX|
               or
   t*v(A) = 5*v(A) + 500
               or
   5*sqrt(2)*v(A) = 5*v(A) + 500
               or
   v(A) = 100*(1+sqrt(2)) ~= 241.42 miles/hour
               and
   v(B) = 50*(2+sqrt(2)) ~= 170.71 miles/hour   
   

  Posted by Bractals on 2007-05-05 11:26:22
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