Kane challenges Tom to a race between two red lights and back. They both start from the same red light but Kane starts when Tom is already halfway across. Kane catches up with Tom at a point 50 meters from the other red light.

Kane continues to the end and turns back and meets Tom only 20 meters from the same red light. He continues running to the starting point and starts running back again to the other end while Tom reaches the other end and starts his return trip.

Assuming they were running at constant speeds, how far from the first red light do Kane and Tom meet for the third time?

Let distance between the lights be x

Speed of Kane =a and Tom = b

1) (x-50)/a=(x/2-50)/b or a/b= (x-50)/(x/2-50)

2) (50+20)/a=(50-20)/b or a/b = 7/3

Hence from 1) and 2) x = 400

for next place they meet. Let it be y mtr from second red light

(20+y)/b=(380+400-y)/a or (780-y)/(20+y)=7/3

y=220 or its 180m from the first red light

Edited on October 9, 2013, 8:59 am

Posted by Salil on 2013-10-09 04:43:28