A 200 m long train crosses a man walking at a speed of 6.6 km/h in the opposite direction in 15 seconds. What is the speed (in km/h) of the train?

Correct Answer: 41.4

Step-by-Step Explanation:

To find the speed of the train, we need to consider the relative speed when two objects move in opposite directions.

Step 1: Understand the given data

Length of the train ($d$) = 200 m
Speed of the man ($v_{\text{man}}$) = 6.6 km/h
Time taken to cross the man ($t$) = 15 seconds

Step 2: Calculate the relative speed

When the train crosses a moving man, the total distance covered is equal to the length of the train. Therefore, the relative speed is given by:

$\text{Relative Speed}=\frac{\text{Distance}}{\text{Time}}$

$\text{Relative Speed}=\frac{200}{15}\text{m/s}$

Step 3: Convert the relative speed from m/s to km/h

To convert speed from meters per second (m/s) to kilometers per hour (km/h), multiply by $\frac{18}{5}$:

$\text{Relative Speed (in km/h)}=\frac{200}{15}\times \frac{18}{5}$

$\text{Relative Speed (in km/h)}=\frac{40\times 18}{15}=\frac{720}{15}=48\text{km/h}$

Step 4: Find the speed of the train

Since the train and the man are moving in opposite directions, their relative speed is the sum of their individual speeds:

$\text{Relative Speed}=v_{\text{train}}+v_{\text{man}}$

Substituting the known values:

$48=v_{\text{train}}+6.6$

$v_{\text{train}}=48-6.6=41.4\text{km/h}$

Thus, the speed of the train is 41.4 km/h.