A train passes a 40 m long bridge in 15 seconds and a watchman in 7 seconds. Find the length of the train.

1. Problem Description

A train passes a 40 m long bridge in 15 seconds and a watchman in 7 seconds. Find the length of the train.

2. Solution Steps

Let $L$ be the length of the train (in meters) and $v$ be the speed of the train (in meters per second).

We have two equations:

The train passes a 40 m bridge in 15 seconds, so:

$\frac{L + 40}{v} = 15$

The train passes a watchman in 7 seconds, so:

$\frac{L}{v} = 7$

We can express $v$ from the second equation:

$v = \frac{L}{7}$

Substitute this into the first equation:

$\frac{L + 40}{\frac{L}{7}} = 15$

$\frac{7(L + 40)}{L} = 15$

$7(L + 40) = 15L$

$7L + 280 = 15L$

$280 = 15L - 7L$

$280 = 8L$

$L = \frac{280}{8}$

$L = 35$

Thus, the length of the train is 35 meters.

3. Final Answer

D. 35 M