Q 2 towns A & B are connected by regular bus service with a bus leaving in either direction in every T minute. A man cycling with a speed of 20 km/h in a direction A to B, notice that a bus goes passed him every 18 min in the direction of his motion & every 6 min in opposite direction. What is period T of the bus service and with what speed do the buses ply on the road?
Asked by Sourav Ganguly | 12th Jul, 2013, 03:57: PM
Let V be the speed of the bus running between towns A and B.
Speed of the cyclist, v = 20 km/h
Relative speed of the bus moving in the direction of the cyclist
= V v = (V 20) km/h
The bus went past the cyclist every 18 min i.e.,
(when he moves in the direction of the bus).
Distance covered by the bus =
(i)
Since one bus leaves after every T minutes, the distance travelled by the bus will be equal to 
Both equations (i) and (ii) are equal.

Relative speed of the bus moving in the opposite direction of the cyclist
= (V + 20) km/h
Time taken by the bus to go past the cyclist 

From equations (iii) and (iv), we get

Substituting the value of V in equation (iv), we get

Let V be the speed of the bus running between towns A and B.
Speed of the cyclist, v = 20 km/h
Relative speed of the bus moving in the direction of the cyclist
= V v = (V 20) km/h
The bus went past the cyclist every 18 min i.e., (when he moves in the direction of the bus).
Distance covered by the bus =
(i)
Since one bus leaves after every T minutes, the distance travelled by the bus will be equal to
Both equations (i) and (ii) are equal.
Relative speed of the bus moving in the opposite direction of the cyclist
= (V + 20) km/h
Time taken by the bus to go past the cyclist
From equations (iii) and (iv), we get
Substituting the value of V in equation (iv), we get
Answered by | 12th Jul, 2013, 04:48: PM
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