Question

A train crosses a platform 150m long in 15 seconds and crosses a pole in 7.5 seconds. What is the speed of the train in km/hr?

Hint:

To convert from m/s to km/hr, multiply by \( \frac{18}{5} \).

Answer 1

Step 1: Understanding the question.
We are asked to find the speed of the train. The train crosses a platform and a pole, giving us two pieces of information about the distance and time.
Step 2: Calculating the speed of the train.
Let the length of the train be \( L \).
- When the train crosses the pole, the distance traveled is equal to the length of the train, and the time taken is 7.5 seconds. Therefore,
\[ \text{Speed of the train} = \frac{L}{7.5} \] - When the train crosses the platform, the distance traveled is the sum of the length of the train and the length of the platform, and the time taken is 15 seconds. Thus,
\[ \text{Speed of the train} = \frac{L + 150}{15} \] Since the speed of the train is the same in both cases, we can set the two expressions equal to each other: \[ \frac{L}{7.5} = \frac{L + 150}{15} \] Step 3: Solving for \( L \).
Cross-multiply to solve for \( L \): \[ 15L = 7.5(L + 150) \] \[ 15L = 7.5L + 1125 \] \[ 7.5L = 1125 \] \[ L = 150 \, \text{m} \] Step 4: Finding the speed.
Now that we know the length of the train, we can calculate the speed using the formula: \[ \text{Speed of the train} = \frac{L}{7.5} = \frac{150}{7.5} = 20 \, \text{m/s} \] To convert this into km/hr: \[ \text{Speed in km/hr} = 20 \times \frac{18}{5} = 72 \, \text{km/hr} \] Step 5: Conclusion.
The speed of the train is 72 km/hr.