two towns A & B are connected by regular bus service with a bus leaving in either direction every T minute.A man cycling with a speed of 20km/h in the direction A to B notices that a bus goes past him every 18 minutes in the direction of his motion ,and every 6 minute in the opposite direction.what is the period T of the bus service and with what speed do the buses ply on the road?
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Cyclist speed is 20 km/h
Time interval between buses in either direction is T minutes.
Let the velocity of the bus be V m/s.
We know that the buses have a constant distance between them, since their speed is constant and the time period T is the same.
So, S = (V +20) x 6
and S = (V-20) x 18.
6V +120 = 18V - 360
12V = -480
V = + or - 40 km/h.
S = 60 x 6/60 = 6 km.
T = 6x60/40 = 9 minutes.
Time interval between buses in either direction is T minutes.
Let the velocity of the bus be V m/s.
We know that the buses have a constant distance between them, since their speed is constant and the time period T is the same.
So, S = (V +20) x 6
and S = (V-20) x 18.
6V +120 = 18V - 360
12V = -480
V = + or - 40 km/h.
S = 60 x 6/60 = 6 km.
T = 6x60/40 = 9 minutes.