Two towns A and B are connected by a regular bus services with a Bus leaving in either direction every T minutes . A man cycling with A speed of 20Kmh-1 in the direction A and B notices that a bus goes
past him every 18m in the direction of his motion and every 6 m 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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ANSWER :
☞ Let v kmph be the constant speed with which the bus travel ply between the towns A and B.
☞ Relative velocity of the bus from A to B wrt the cyclist = (v-20) kmph
☞ Relative velocity of the bus from B to A wrt the cyclist = (v+20) kmph
☞ Distance travelled by the bus in time T (minutes) = vT
▶ As per Question :
→ vT/v-20 = 18
→ vT = 18v - 18×20 .......... (1)
→ vT/v+20 = 6
→ vT = 6v + 20×6 ......... (2)
Equating (1) and (2), we get
18v - 18×20 = 6v + 20×6
12v = 20×6 + 18×20
12v = 480
v = 40kmph
Putting this value of v in (1), we get
40T = 18×40 - 18×20 = 18×20
T = 18×40/40
T = 9min
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