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Milestone Muse (Posted on 2013-10-10) Difficulty: 3 of 5
Two cars leave simultaneously from points X and Y on the same road but in opposite directions. Their speeds are constant, and in the ratio 5 to 4 with the car leaving at X being the faster of the two.

The cars travel to and fro between X and Y. They meet for the second time at the 145th milestone and for the third time at the 201st milestone.

What are the respective milestones at X and Y?

No Solution Yet Submitted by K Sengupta    
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Solution Another approach Comment 3 of 3 |
Let the milestones at X and Y show x and y, so that the distance from
X to Y is y x miles. At any stage, the distances travelled by the cars
must be in the ratio 5:4. Thus, at the 2nd and 3rd meetings:

(y x) + (y 145)  = 5/4
(y x) + (145 x)                     giving    2x + y = 435   (1)

2(y x) + (201 x)  = 5/4
2(y x) + (y 201)                   giving    2x + 7y = 1809  (2)

Solving (1) and (2) simultaneously gives  x = 103 and y = 229.

  Posted by Harry on 2013-10-14 20:24:34
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