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?
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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