Two trains are traveling in opposite directions. Train A is moving at a speed of 63 kilometers per hour and can cross a platform that is 199.5 meters long in 21 seconds. If Train B is 157 meters long and traveling at 54 kilometers per hour in the opposite direction, how many seconds would it take for Train A to completely cross Train B from the moment they meet?

Question

Accepted Answer

To solve this problem, we first need to determine the length of Train A.

When Train A crosses the platform, the total distance covered is equal to the length of the train plus the length of the platform:
$$
	ext{Speed of Train A} = 63 	ext{ kmph} = \frac{63 	imes 5}{18} = 17.5 	ext{ m/s}
$$

Using the formula: 
$$
	ext{Time} = \frac{	ext{Distance}}{	ext{Speed}}
$$

We can write:
$$
21 = \frac{x + 199.5}{17.5}
$$

Where $x$ is the length of Train A. Solving for $x$:
$$
21 	imes 17.5 = x + 199.5
$$
$$
367.5 = x + 199.5
$$
$$
x = 367.5 - 199.5 = 168 	ext{ meters}
$$

Next, we calculate the relative speed of the two trains. Since they're moving in opposite directions, we add their speeds:
$$
	ext{Relative speed} = 17.5 + 15 = 32.5 	ext{ m/s}
$$

The total distance required for the trains to completely cross each other is the sum of their lengths:
$$
	ext{Required time} = \frac{	ext{Length of Train A + Length of Train B}}{	ext{Relative speed}} = \frac{168 + 157}{32.5} = \frac{325}{32.5} = 10 	ext{ seconds}
$$

Therefore, Train A would take 10 seconds to completely cross Train B from the moment they meet.

Answer

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