    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 20  km/h , the time in which the bus passes the cyclist in his direction of motion is 18 min and in opposite to his direction is 6 min . Let v b be the speed of the bus between towns A and B and v c be the speed of the cyclist. The relative speed of the bus is, v= v b − v c The distance covered by the bus is, d=( v b − v c )×18 min =( v b − v c )×18 min× 1 s 60 min =( v b − v c )× 18 60 …… (1) Let T be the time in which every bus leaves from the bus stop. The distance covered by the bus is, D= v b × T 60 …… (2) Equate equation (1) and (2). ( v b − v c )× 18 60 = v b × T 60 …… (3) The relative velocity of the bus in opposite the motion of the cycle is v b + v c . In this case the distance covered by the bus is, D=( v b + v c )×6 min …… (4) Equate the equation (2) and (4). ( v b + v c )×6 min= v b × T 60 ( v b + v c )× 6 60 = v b × T 60 …… (5) Divide equation (3) by (5). ( v b − v c )× 18 60 ( v b + v c )× 6 60 = v b × T 60 v b × T 60 Substitute the required values in the above expression. ( v b −20  km/h )× 18 60 ( v b +20  km/h )× 6 60 =1 v b =40  km/h Substitute the required values in equation (5). ( 40  km/h +20  km/h )× 6 60 =40  km/h × T 60 T=9 min 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.  Suggest Corrections  0      Explore more