Two trains of length 100m and 250m run on parallel lines

The answer is 20 m/s.

Let the faster train run at x m/s and the slower train run at y m/s.

The first statement states that it will take 70 seconds to cross each other running in the same direction. The first important thing her is that the faster train is behind the slower train, otherwise they would never cross. Secondly, in order to cross the slower train, the faster train will need to cover 350m MORE (250 m + 100 m) in the 70 seconds than the other train.

\(\frac{350}{(x - y)} = 70\)

\(\frac{5}{(x - y)} = 1\)

\(5 = x - y\) (Equation 1)

The second statement states that it will take 10 seconds to cross each other running in the opposite direction. The difference between this and running in the same direction, is that the slower train's speed CONTRIBUTES to the cross rather than inhibiting it. If the slower train was standing still, the faster train would take (350/x) seconds to pass it. Since the slower train is moving in the other direction though, it will take (350/ x+y) seconds to cross.

\(\frac{350}{(x + y)} = 10\)

\(\frac{35}{(x + y)} = 1\)

\(35 = x + y\) (Equation 2)

Solving these two equations, you get x = 20 m/s, and y = 15 m/s.