Problem Solving

swerve wrote:A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train traveling at the same velocity passes a platform in 3t seconds then what is the length of the platform?

A. 0.5 L
B. L
C. 1.5 L
D. 2 L
E. 3 L

We can let p = the length of the platform in meters and r = the rate the train is traveling.

When we say the train crosses a platform in 3t seconds, it really means it takes 3t seconds for the nose of the train to enter one end of the platform and the tail of the train to exit the other end of the platform. Thus, in 3t seconds, not only does the train travel the entire length of the platform but also it travels its body length L. Thus, we have (using time x rate = distance formula):

3t * r = p + L

We are also given that the train crosses a pole (notice that the pole has a negligible width) in t seconds. So when the train crosses the pole, it only travels its body length in t seconds. Thus we have:

t * r = L

Subtracting these two equations, we have:

2tr = p

Since L = tr, and p = 2tr, then p = 2L.

Answer: D