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 ?

Explanation

Supose, constant speed of but is v km/h
Speed of cyclist is 20 km/h
Speed of bus from A to B w.r.t cycle,
`(v-20) km h ^(-1)` (In direction of cycle)
Speed of bus, from B to A w.r.t. cycle,
`(v + 20) km h ^(-1)` (In direction of cycle )
Distance covered in time "T" by bus,
`(vT)/(v - 20) = 18`
`therefore vT =18 v - 18 xx 20 " "...(1)`
`and (vT)/(v + 20) = 6`
`therefore vT = 6 v + 6 xx 20 " "...(2)`
`therefore ` By comparing equation (1) and (2),
`18 v-18 xx 20 = 6v + 6 xx 20`
`therefore 12 v = (18 + 6) xx 20`
`therefore 12v =24 xx 20`
`therefore v = 40 km//h`
Now, from equation (1),
`40T = 18 xx -18 xx 20`
`= 720 -360`
`=360 =9 hr`