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

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Solution

Given, the speed of the cycle is

Let

The relative speed of the bus is,

The distance covered by the bus is,

Let

The distance covered by the bus is,

Equate equation (1) and (2).

The relative velocity of the bus in opposite the motion of the cycle is

Equate the equation (2) and (4).

Divide equation (3) by (5).

Substitute the required values in the above expression.

Substitute the required values in equation (5).

Thus, the *T* of the bus service is 9 min, and the speed at which the buses ply on the road is 40 km/h.

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