# What is the relation between the speeds of the two boats?

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A car M starts from point A and a car N starts from point B and move towards opposite sides at a constant speed. The cars meet 500 yards from A for the first time. After reaching the opposite points, each of the car returns back without any break and this time, they meet 300 yards from B.

What is the distance between the two points A and B and what is the relation between the speeds of the two boats?

posted Mar 10, 2014

Let the distance between points A and B be d.
When they meet for the first time, car M has traveled 500 while car N has traveled (d-500).
As time taken by both is the same to travel the respective distances , and calculating d as a multiple of 100 to simplify
=> Speed of M/ Speed of N = 5/(d-5)

The next time they meet car M has traveled (d-500)+ 300, while car N has traveled 500 + d-300
=> Speed of M/ Speed of N = (d-2)/ (d+2)

Equating them both we get => 5(d+2)= (d-5)(d-2) => d=12

Thus distance between the two points in 1200.
Speed of M/Speed of N = 5/(12-5)= 5/7

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