question_answer 9)

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T min. A man cycling with a speed of  in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road ?  

Answer:

Let speed of each bus For buses going from town A to B: Relative speed of a bus in the direction of motion of the man Buses plying in this direction go past the cyclist after every 18 min.  Distance covered   Since a bus leaves the town after every T mm, so the above distance covered                                       ?(i) For buses going from town B to A: Relative speed of bus in the direction opposite to the motion of the man   Buses going in this direction go past the cyclist after every 6 min, therefore                         ?(ii) Dividing (i) by (n), we get   or            or          . From equation (ii),   or            .