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Two trains P and Q are running in opposite directions with speeds of 72 km/hr and 54 km/hr, respectively. If the length of train P is 300 m and they cross each other in 12 seconds, what is the length of train Q?
120 m
150 m
200 m
180 m
120 m
Calculate relative speed in m/s immediately: (72+54)├Ч185тАЛ=126├Ч185тАЛ=7├Ч5=35 m/s. Total distance = 35├Ч12=420 m. Subtract the known train length: 420тИТ300=120 m.
Speed of train P = 72 km/hr, speed of train Q = 54 km/hr, length of train P = 300 m, time taken to cross = 12 seconds.
LPтАЛ+LQтАЛ=(VPтАЛ+VQтАЛ)├ЧT├Ч185тАЛ
Calculate relative speed in m/s immediately: (72+54)├Ч185тАЛ=126├Ч185тАЛ=7├Ч5=35 m/s. Total distance = 35├Ч12=420 m. Subtract the known train length: 420тИТ300=120 m.
Failing to convert km/hr to m/s, or forgetting that total distance covered equals the sum of the lengths of both trains.
Calculate relative speed in m/s
Since the trains move in opposite directions, their relative speed is the sum of their individual speeds. Convert to m/s by multiplying by 185тАЛ.
(72+54)├Ч185тАЛ=126├Ч185тАЛ=35┬аm/s
Calculate total distance covered
Total distance is the sum of lengths of both trains, calculated using Distance=Relative┬аSpeed├ЧTime.
DtotalтАЛ=35├Ч12=420┬аm
Determine the length of train Q
Subtract the length of train P from the total distance.
LQтАЛ=420тИТ300=120┬аm
A is correct because the total distance covered by both trains is 420 m, and subtracting the 300 m length of train P leaves 120 m for train Q.
This concept of relative speed is frequently used in 'Boats and Streams' problems; remember that relative speed adds for opposite directions and subtracts for the same direction.