Question

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 Tof the bus service and with what speed (assumed constant) do the buses ply on the road?

Answer 1

Let the speed of the bus be v kmh^-1

Distance covered by one bus before the next one leaves the same town is vT For buses going in the same direction as the cyclist, frequency of the bus is 18 min i.e.,

vT/relative velocity of the bus w.r.t. the cyclist = 18 min

vT/(v - 20) = 18 … (1)

Similarly, for buses going in the opposite direction, frequency of the bus = 6 min

vT/relative velocity of the bus w.r.t. the cyclist = 6 min

vT/(v + 20) = 6 … (2)

(1)/(2)

⇒ (v + 20)/(v - 20)

Substitute for v in (1)

(40 x T)/(40 - 20) = 18

⇒ T = 9 min.