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A policeman and a thief start from the same place and walk at the rate of 5┬аkm/h and 5.5┬аkm/h, respectively. How much time will they take to be 9.5┬аkm apart, if they walk in the same direction?
17 hrs
4 hrs 15 min
2 hrs 55 min
19 hrs
19 hrs
Since both are moving in the same direction, the relative speed is the difference between their speeds. Just divide the total distance by the difference: 9.5 / (5.5 - 5) = 9.5 / 0.5 = 19.
Policeman speed v1 = 5 km/h, Thief speed v2 = 5.5 km/h, distance between them d = 9.5 km. They walk in the same direction.
t=тИгv2тАЛтИТv1тАЛтИгdтАЛ
Since both are moving in the same direction, the relative speed is the difference between their speeds. Just divide the total distance by the difference: 9.5 / (5.5 - 5) = 9.5 / 0.5 = 19.
Students often add the speeds (5 + 5.5) as if they were moving in opposite directions, resulting in an incorrect time.
Calculate Relative Speed
Since the policeman and thief are moving in the same direction, their relative speed is the difference between their individual speeds: vrelтАЛ=5.5тИТ5=0.5 km/h.
vrelтАЛ=5.5┬аkm/hтИТ5┬аkm/h=0.5┬аkm/h
Apply Time Formula
Use the formula t=vrelтАЛdтАЛ to find the time taken to reach a distance of 9.5 km.
t=0.59.5тАЛ=19┬аhours
D is correct because the relative speed is 0.5 km/h and the required time is 19 hours.
This concept of relative speed is fundamental in problems involving trains crossing, circular tracks, and boat-stream dynamics.
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