The distance between two stations A and B is 200 km. A train from A to B at a unifrom speed of `60 km h^(-1)` , After half an hour another train leaves B towards, A with a unifrom speed of `80 km h^(-1)` , Determine the distance of the point from A where the two train s meet each other.

Explanation

Let the two trains meet at a distance of x km from A.

Speed = `("distance")/("time")`
Time taken for the train which starts from A is
time = `("distance")/("speed")=x/60`
Time taken for the train which starts from B is
time = `((200-x))/80h`
Difference in the time is equal to `1/2` hour.
`x/60-(200-x)/80=1/2`
`(80x-60(200-x))/(60xx80)=1/2`
`(80x-12000+60x)/4800=1/2`
140x - 12000 = 2400
140 x = 14400
x = 102.68 km