Two trains pass each other in 10 seconds when moving in opposite directions. When moving in the same direction, the swifter train passes the slower one in 25 seconds. What is the speed of each train if their respective lengths are 300 meters and 500 meters? Thank you.
Well...if by "passing" you mean that the trains completely pass each other.......
Call the rate of the slower train R1 and call the rate of the faster train R2.......and these are in m/sec
Then when passing each other, the distance that the back of the either train must cover in 10 seconds is 800m....but either train is covering this distance by the combined rate of both trains
So....we have
Total distance to be covered / [ combined rates] = total time
800 / [ R2 + R1] = 10 → 800 = 10R2 + 10R1 → 80 = R2 + R1 (1)
And....when the trainns are going in the same direction we have that the effective rate of the faster train is being slowed by the rate of the slower train
800 / [ R2 - R1] = 25 → 800 = 25R2 - 25R1 → 32 = R2 - R1 (2)
Adding (1) and (2), we have
112 = 2R2 divide both sides by 2
56 = R2 = 56 m/sec = 201.6 km/h ....this is the rate of the faster train
And the slower train moves at 80 = 56 + R1 → R1 = 24m/sec = 86.4 km/hr
Proof :
If the slower train were standing still, it would take the back of the faster train about 14 + 2/7 seconds to cover 800m ....but ...its rate is effectively being "slowed" by the rate of the slower train......so...its effective rate is only [ 56 - 24] = 32m/s
And 25 sec * 32 m/s = 800 m
