A train of length 150 m takes 10 seconds to cross another train 100 m long coming from the opposite direction . If the speed of first train is 30 km / hr, what is the speed of second train?
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Question: A train of length 150 meters takes 10 seconds to cross another train 100 meters long coming from the opposite direction. If the speed of the first train is 30 km/h, what is the speed of the second train?
Choices:
The correct answer is: 60 km/h
<h2>Explanation:</h2>To solve this problem, we need to use the concepts of relative speed and the distance covered while crossing each other.
Let's denote the speed of the second train as \( v_2 \) in km/h. When two trains cross each other coming from opposite directions, their relative speed is the sum of their individual speeds.
<h3>Step-by-Step Solution:</h3> <h4>Step 1: Convert the speed of the first train</h4>The speed of the first train is given as 30 km/h. To work with SI units, we convert this speed to meters per second (m/s).
\[ \text{Speed of first train} = 30 \, \text{km/h} = \frac{30 \times 1000}{3600} \, \text{m/s} = 8.33 \, \text{m/s} \]
<h4>Step 2: Calculate the total distance covered while crossing</h4>The two trains are crossing each other, so the total distance covered is the sum of their lengths:
\[ \text{Total distance} = 150 \, \text{m} + 100 \, \text{m} = 250 \, \text{m} \]
<h4>Step 3: Use the time taken to cross each other</h4>The problem states that it takes 10 seconds for the trains to cross each other.
<h4>Step 4: Calculate the relative speed</h4>The relative speed in meters per second (m/s) can be calculated using the formula for speed:
\[ \text{Relative speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{250 \, \text{m}}{10 \, \text{s}} = 25 \, \text{m/s} \]
<h4>Step 5: Determine the speed of the second train</h4>Let the speed of the second train be \( v_2 \) in m/s. The relative speed is the sum of the speeds of the two trains:
\[ \text{Relative speed} = \text{Speed of first train} + \text{Speed of second train} \]
Substituting the known values:
\[ 25 \, \text{m/s} = 8.33 \, \text{m/s} + v_2 \]
Solve for \( v_2 \):
\[ v_2 = 25 \, \text{m/s} - 8.33 \, \text{m/s} = 16.67 \, \text{m/s} \]
<h4>Step 6: Convert the speed back to km/h</h4>To convert the speed back to km/h, we use the conversion factor:
\[ v_2 = 16.67 \, \text{m/s} \times \frac{3600}{1000} \approx 60 \, \text{km/h} \]
<h3>Conclusion</h3>The speed of the second train is indeed 60 km/h, making option C the correct choice.
Understanding the steps and formulas used in this explanation is crucial for solving similar problems involving relative speed and distance calculations.
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