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Question

A 145 m long train crosses a man walking at a speed of 9.5 km/h in the opposite direction in 30 seconds. What is the speed (in km/h) of the train?

The correct answer is

7.9

To find the speed of the train, we first need to determine the relative speed between the train and the man walking in the opposite direction. The man's speed is given as 9.5 km/h.

Since both are moving in opposite directions, we add their speeds to get their relative speed.

Let the speed of the train be x km/h.

Relative speed = (Speed of train + Speed of man walking) = x + 9.5 km/h.

The train covers a distance equal to its length in 30 seconds. The length of the train is 145 meters, which we convert to kilometers: 145 m = 0.145 km.

Using the formula for speed, \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \), where time is in hours, we need to convert 30 seconds to hours: 30 seconds = \(\frac{30}{3600}\) hours.

Now we set up the equation for relative speed:

Relative speed = \(\frac{0.145}{\frac{30}{3600}}\) km/h.

Simplifying the equation:

\(\frac{0.145 \times 3600}{30} = 17.4\) km/h.

Thus, \(x + 9.5 = 17.4\).

Solving for x gives:

\(x = 17.4 - 9.5 = 7.9\) km/h.

Therefore, the speed of the train is 7.9 km/h.

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Important Questions from Speed Time and Distance

  1. The average speed of a train is 180% of the average speed of a car. The car covers a distance of 990 km in 15 hours. The time taken (in hours) by the train to cover the distance of 891 km is:

  2. If Rohit can cover a distance of 1188 km in 22 hours, then what is the speed of Rohit?

  3. A train is moving at 72 km/hrs. The distance covers in 15 minutes by the train is:

  4. If Sonu is driving a car at a speed of 20 m/s, then in how much time Sonu will cover a distance of 936 km?

  5. A person crosses a 1600 m long street in 4 min. What is his speed (in km/h)?

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