Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of `20 km h^(-1)` 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

9 min, 40 km `hr^(-1)`

Explanation

`(V_(B)T)/(V_(B)-20)=18, (V_(B)T)/(V_(B)+20)=6, (V_(B)+20)/(V_(B)-20)=3`

`rArr V_(B)+20=3V_(B)-60 v_(B)=40 km//h`
`:. T=(6(V_(B)+20))/(V_(B))=(6xx60)/(40)=9 min`