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### Distance Speed Problem

Distance Speed Problem - 27 February

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?

1. Well I ended using up 5 simultaneous equations considering frames of reference and relative velocities which was a bit tedious. The answers are as follows:
Total distance = 1200 yards
Speed of car A = 1.063
Speed of car B = 1.488
Making the speed of car B equivalent to 7/5 of car A's speed

2. Total distance from A point to B Point is 700 Yards and relation between the speed of car M and N is respectively 5:6.

3. Total distance from A point to B Point is 700 Yards and relation between the speed of car M and N is respectively 2:5.

4. What is the distance between the two points A and B and what is the relation between the speeds of the two BOATS?

BOATS?!!

5. "Boats". Yes, the poster of the question most likely modified an old Marilyn Vos Savant Parade Magazine puzzle that used boats instead of cars and forgot to change one of the words.