Question

A car A starts from a point P towards another point Q. Another car B starts (also from P) 1H after the first car and overtakes it after covering 30% of the distance PQ. After that, the cars continues. On reaching Q, car B reverses and meets car A, after covering 70/3 of the distance QP. Find the time taken by car B to cover the distance PQ ( in hours) .

Answer 1

Let the distance between the point P and Q= a

When B overtakes A for the first time, both of them cover 3a/10.

When B meets A after that, it (B) covers (7a/10+7a/30) or 28a/30,

while A covers (23a/30 – 9a/30) or 14a/30.

Therefore, B is twice as fast as A.

A starts 1 H after B, it catches up with in 1 H. Therefore, covers 0.3a in 1 H. or x in 10/3H