Question

A 120 m long train crosses a man walking at a speed of 8.5 km/h in the opposite direction in 12 seconds. What is the speed (in km/h) of the train?

• A. 23.3
• B. 27.5
• C. 29.1
• D. 31.5

Answer 1

Answer:

B. 27.5

The speed of the train is 27.5 km/h

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* Step 1: Find the relative speed in meters per second (m/s)

When a train crosses a moving man, the total distance covered equals the length of the train.

$\text{Relative Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{120\text{ m}}{12\text{ seconds}} = 10\text{ m/s}$

* Step 2: Convert the relative speed to kilometers per hour (km/h)

To convert m/s to km/h, multiply by $\frac{18}{5}$.

$\text{Relative Speed} = 10 \times \frac{18}{5} = 36\text{ km/h}$

* Step 3: Calculate the train's actual speed

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

$\text{Relative Speed} = \text{Speed of Train} + \text{Speed of Man}$

$36\text{ km/h} = \text{Speed of Train} + 8.5\text{ km/h}$

$\text{Speed of Train} = 36 - 8.5 = \mathbf{27.5\text{ km/h}}$