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 `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`