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Two trains of length 120┬аm and 280┬аm are running towards each other on parallel lines at 42┬аkm/h and 30┬аkm/h, respectively. In how much time will they be clear of each other from the moment they meet?
21 sec
25 sec
20 sec
10 sec
20 sec
Convert speed from km/h to m/s using (5/18) once: VrelтАЛ = (42 + 30) * (5/18) = 72 * (5/18) = 20 m/s. Then time = Total length / VrelтАЛ = (120 + 280) / 20 = 400 / 20 = 20 seconds.
Length of train 1 (L1) = 120 m, Speed 1 (V1) = 42 km/h. Length of train 2 (L2) = 280 m, Speed 2 (V2) = 30 km/h. They are moving towards each other (opposite direction).
t=V1тАЛ+V2тАЛL1тАЛ+L2тАЛтАЛ
Convert speed from km/h to m/s using (5/18) once: VrelтАЛ = (42 + 30) * (5/18) = 72 * (5/18) = 20 m/s. Then time = Total length / VrelтАЛ = (120 + 280) / 20 = 400 / 20 = 20 seconds.
Forgetting to add the lengths of both trains (total distance = L1 + L2) or failing to convert km/h to m/s before dividing.
Calculate Total Distance
Since the trains are crossing each other, the total distance to cover is the sum of their lengths: D=120+280=400┬аm.
D=400┬аm
Calculate Relative Speed
Since the trains are moving in opposite directions, their relative speed is the sum of their individual speeds: VrelтАЛ=42+30=72┬аkm/h.
VrelтАЛ=72┬аkm/h
Convert Speed to m/s
To match the unit of distance (meters), convert speed from km/h to m/s by multiplying by 5/18: 72├Ч(5/18)=20┬аm/s.
VrelтАЛ=20┬аm/s
Calculate Time
Apply the time formula t=D/VrelтАЛ: t=400/20=20┬аseconds.
t=20400тАЛ=20┬аs
C is correct because the total distance of 400 m covered at a relative speed of 20 m/s results in exactly 20 seconds.
This concept is a staple in Time-Speed-Distance problems; always check if trains are moving in the same (subtract speeds) or opposite (add speeds) direction.
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