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:

Both crossings involve the same train speed and the same train length. Write distance = speed times time for each case, then think about what happens when you subtract one equation from the other, since the train's own length cancels out and leaves you with something you can solve directly.

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.

Answer 2

Concept:

• When a train crosses an object, the distance covered equals speed multiplied by time, where the distance is the length of the train plus the length of the object (zero for a pole).
• If the speed stays constant in both situations, subtracting the two distance equations removes the unknown train length directly, giving the speed without solving for the length first.

Step 1: Write the two distance equations
Let the speed of the train be $v$ m/s and the length of the train be $L$ metres.
Crossing the pole: distance covered = length of train, so $L = v \times 7.5$
Crossing the platform: distance covered = length of train plus length of platform, so $L + 150 = v \times 15$

Step 2: Subtract the two equations to remove $L$
$(L + 150) - L = v \times 15 - v \times 7.5$
$150 = v \times 7.5$

Step 3: Solve directly for the speed
$v = \frac{150}{7.5} = 20 \, \text{m/s}$

Step 4: Convert the speed to km/hr
$v = 20 \times \frac{18}{5} = 72 \, \text{km/hr}$

Final Answer: The speed of the train is 72 km/hr.