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

+1 vote
381 views

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

Similar Puzzles

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then what is the speed of the first train ?

A black boat is on shore A and a purple boat is on the opposite shore B of a lake. Each boat starts at the same time for the opposite shore.

The boats meet and pass each other 500 units from shore A. Each boat gets to the opposite shore and immediately starts a return journey. The two boats then meet and pass 300 units from shore B.

How long is the lake, and what is the ratio of speeds between the purple and black boats?