Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man ccling with a speed of `20 km h^(-)` 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 oppsite direction. What is the period T of the bus service and with what speed (assi,ed cpmstant) do the buses ply on the rod?

Explanation

Speed of each bus `v kmh^(-1)`. Relative velocity of the bus w.r.t. cyclist `= v- 20 kmh^(-1)` for A to B and `(v+20) kmh^(-1)` for B to A trip. Distance travelled by the bus in time `T= vT. vT"/"v-20= 18, vT"/"v+20= 6`, solving `v= 40 kmh^(-1)` and T= 9 min.