Question

175 m long train crosses another train of length 100 m in 15 sec, running in same direction. If the speed of the first train is 90 km/hr, then find the speed of the second train (in km/hr)?

• A. 35 km/hr
• B. 42 km/hr
• C. 24 km/hr
• D. 30 km/hr

Answer 1

The Correct Option is C

To find the speed of the second train, let's follow these steps:

1. **Convert Speed Units:** The speed of the first train is given as 90 km/hr. Convert this to meters per second (m/s) using the conversion factor, where 1 km/hr = (5/18) m/s.

\[ \text{Speed of first train in m/s} = 90 \times \frac{5}{18} = 25 \text{ m/s} \]

2. **Relative Speed Calculation:** As the trains are moving in the same direction, the relative speed between them is the difference in their speeds.

3. **Total Length of Trains:** The first train is 175 m long, and the second train is 100 m long. So the total length is: \[ \text{Total length} = 175 + 100 = 275 \text{ m} \]

4. **Time to Cross:** It takes 15 seconds for the trains to cross each other. We use the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

5. **Finding Relative Speed:** The relative speed in m/s is: \[ \frac{275}{15} = 18.33 \text{ m/s} \]

6. **Calculate Speed of Second Train:** Since the relative speed is 18.33 m/s, and the first train moves at 25 m/s, the speed of the second train is: \[ \text{Speed of second train in m/s} = 25 - 18.33 = 6.67 \text{ m/s} \]

7. **Convert Back to km/hr:** Convert the speed back to km/hr using 1 m/s = (18/5) km/hr: \[ 6.67 \times \frac{18}{5} = 24 \text{ km/hr} \]

The speed of the second train is 24 km/hr.