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Two trains, 125 m and 165 m in length, respectively, are running in opposite directions, one at the rate of 80 km/h and the other at the rate of 65 km/h. In how many seconds will they be completely clear of each other from the moment they meet?
7.2 sec
7.5 sec
6.5 sec
6.8 sec
7.2 sec
Calculate relative speed in m/s: (80+65)×185=145×185≈40.27 m/s. Sum lengths: 125+165=290 m. Time = 290/40.27≈7.2 seconds.
Train 1 length L1 = 125 m, speed v1 = 80 km/h; Train 2 length L2 = 165 m, speed v2 = 65 km/h. They travel in opposite directions.
t=vrelL1+L2=(v1+v2)×185L1+L2
Calculate relative speed in m/s: (80+65)×185=145×185≈40.27 m/s. Sum lengths: 125+165=290 m. Time = 290/40.27≈7.2 seconds.
Students often forget to convert km/h to m/s by multiplying by 185 or add the lengths incorrectly.
Calculate Total Distance
Since the trains are passing each other, the total distance to cover is the sum of their lengths.
D=125+165=290 m
Calculate Relative Speed
Since trains are moving in opposite directions, relative speed is the sum of their individual speeds.
Vrel=80+65=145 km/h
Convert Speed to m/s
Multiply by 5/18 to convert km/h to m/s.
Vm/s=145×185=18725≈40.27 m/s
Calculate Time
Use the formula t=D/Vrel.
t=725/18290=725290×18=7.2 seconds
A is correct because the relative speed of 145 km/h equals 40.27 m/s, and dividing the total distance of 290 m by this speed yields exactly 7.2 seconds.
This concept is fundamental to Time, Speed, and Distance problems. Always remember: add speeds for opposite directions, subtract for same directions.
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