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RECTIONS for question 6: Type in your answer in the input box provided below the question.Two trains, of lengths 500 m and 300 m respectively, run on parallel tracks. When the trains run in the same direction, the faster train takes 80 seconds to cross the slower train. When they run in opposite directions, they take 20 seconds to cross each other. Find the speed (in km/hr) of the slower train.

Question

RECTIONS for question 6: Type in your answer in the input box provided below the question.Two trains, of lengths 500 m and 300 m respectively, run on parallel tracks. When the trains run in the same direction, the faster train takes 80 seconds to cross the slower train. When they run in opposite directions, they take 20 seconds to cross each other. Find the speed (in km/hr) of the slower train.

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Solution

Let's denote the speed of the faster train as F (in m/s) and the speed of the slower train as S (in m/s).

  1. When the trains run in the same direction, the relative speed is (F-S). The time taken to cross each other is the total length of the trains divided by the relative speed. So, we have the equation:

    500m + 300m = (F - S) * 80s 800m = (F - S) * 80s 10m/s = F - S ...(Equation 1)

  2. When the trains run in the opposite direction, the relative speed is (F+S). The time taken to cross each other is the total length of the trains divided by the relative speed. So, we have the equation:

    500m + 300m = (F + S) * 20s 800m = (F + S) * 20s 40m/s = F + S ...(Equation 2)

  3. Now we have a system of two equations. We can solve it by adding the two equations:

    10m/s + 40m/s = F - S + F + S 50m/s = 2F F = 25m/s

  4. Substitute F = 25m/s into Equation 1:

    10m/s = 25m/s - S S = 25m/s - 10m/s S = 15m/s

  5. Convert the speed of the slower train from m/s to km/hr by multiplying by 3.6:

    S = 15m/s * 3.6 = 54 km/hr

So, the speed of the slower train is 54 km/hr.

This problem has been solved

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