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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. A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is

  2. Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.

  3. Rohit and Dinesh are 64 km apart. Rohit can walk at a speed of 15 km/hr and Dinesh at the speed of 17 km/hr. In how many hours will they meet if they are travelling towards each other?

  4. Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:

  5. A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?

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