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 post him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is
Text Solution
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Let v 
be the constant speed with which the buses ply between the towns A and B.
Relative velocity of the bus from A to B with respect to the cyclist
= (v – 20) km 
Relative velocity of the bust form B to A with respect to the cyclist
= (v + 20) km 
Distance travel by the bus in time T (minutes) = Vt
As per questions
Or vT = 18v - 18 × 20 …….(i)
And 
Or vT = 6v+ 20 × 6 ……..(ii)
Equating (i) and (ii), we get
18v – 18 × 20 = 6v + 20 × 6
Or 12v = 20 × 6 + 18 × 20 = 480 or v = 40 km 
Putting this value of v in (i), we get
40T = 18 × 40 – 18 × 20 = 18 × 20
Or 
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