The speed of one is as much as 2/3 of the speed of the other. Find the speeds of each if they meet after 1.5 hours

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## 1 Answer

If the velocity of one boy is v then the velocity of the other is -⅔v, where minus indicates the opposite direction. Their difference in speed is v-(-⅔v)=5v/3.

The distance between them was 7.5km, so if it took 1.5hrs (3/2hrs) for them to meet, 7.5=(5v/3)(3/2)=5v/2, v=(2/5)(7.5)=3kph, and ⅔ of this is 2kph.

So the boys were moving at 2 and 3 kph.

Another way of solving this problem is to consider the boys at each end of the line AB=7.5km. The boy at A is moving with speed v and the boy at B is moving at speed ⅔v towards him. When they meet 1.5hrs later at a point x km from A, x=1.5v. 7.5-x=1.5(⅔v)=v, so 7.5-1.5v=v, 7.5=5v/2, v=⅖(7.5)=3kph, and the other boy moves at 2kph.

by Top Rated User (839k points)

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