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?

When the cars first meet, they have traveled a combined distance equal to the 1 length of the distance. When they meet the second time, they have travelled 3 lengths.

The elapsed time and distance for each of the cars is three times. Now when they meet the second time, M has traveled 500x3 = 1500 yards and since, it is 300 yards longer than the total distance between both the points, the distance is 1200 yards.

The ratio of M’s speed to the ratio of N’s speed is equal to the distance that they traveled before they met for the first time.

i.e. 500/(1200 – 500) = 5/7