Tip #2: For problems on 2 trains, use the concept of relative velocity
1. If two trains of length a and b are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other = (a + b) / (u + v).
2. If two trains of length a and b are moving in the same direction at u m/s and v m/s, then time taken by the faster train to cross the slower train = (a + b) / (u - v) .
Question: 2 trains of length 137 m and 163 m are running towards each other and speeds 42 km/hr and 48 km/hr respectively. In what time will the two trains cross each other?
Relative velocity = 42 + 48 = 90 km/hr = (90 x 5/18) m/s = 25 m/s. (Opposite directions)
Time taken to cross each other = 300 / 25 = 12 sec.
Question: 2 trains running in opposite directions cross a man standing on the platform in 27s and 17s respectively and they cross each other in 23s. Find the ratio of their speeds.
Let the speeds be x m/s and y m/s respectively.
Then, length of 1st train = 27x and that of 2nd train = 17y.
Time taken to cross each other = (27x + 17y) / (x + y) = 23.
= 27x + 17y = 23x + 23y.
= 4x = 6y.
= x: y = 3 : 2.
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Problems on Trains: Problems on Trains Formulas and Shortcuts, Train Problems in Aptitude Questions with Solutions