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Two trains, each 250 m in length, are running on parallel lines in opposite directions at speeds of 90 km/h and 60 km/h respectively. In how many seconds will they cross each other completely?
15 sec
18 sec
10 sec
12 sec
12 sec
Convert relative speed from km/h to m/s by multiplying by 5/18, then divide total length (500 m) by relative speed (25 m/s) to get 20 seconds. Wait, let's recalculate: 90+60=150 km/h. 150×185=3125 m/s. Total length = 250+250=500 m. Time = 500/(125/3)=500×1253=4×3=12 seconds.
Length of each train L1=L2=250 m, Speed of first train v1=90 km/h, Speed of second train v2=60 km/h running in opposite directions.
t=v1+v2L1+L2
Convert relative speed from km/h to m/s by multiplying by 5/18, then divide total length (500 m) by relative speed (25 m/s) to get 20 seconds. Wait, let's recalculate: 90+60=150 km/h. 150×185=3125 m/s. Total length = 250+250=500 m. Time = 500/(125/3)=500×1253=4×3=12 seconds.
Students often forget to add the lengths of both trains (total distance = 250+250=500 m) or fail to add speeds when trains move in opposite directions.
Calculate Total Distance
When two trains cross each other completely, the total distance to be covered is the sum of the lengths of both trains.
Total Distance=250+250=500 m
Calculate Relative Speed
Since the two trains are running in opposite directions, their relative speed is the sum of their individual speeds.
Relative Speed=90+60=150 km/h
Convert Speed to m/s
Convert the relative speed from km/h to m/s by multiplying by 5/18.
Relative Speed=150×185=3125 m/s
Calculate Time Taken
Divide the total distance by the relative speed in m/s to get the crossing time.
Time=125/3500=500×1253=4×3=12 sec
D is correct because the total distance of 500 m divided by the relative speed of 3125 m/s results in exactly 12 seconds.
In physics and relative motion problems, always ensure consistent units (converting km/h to m/s) before calculating time.
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