2 trains running in oppsite directions cross a stationary lady standing at a point named F in 26 seconds and 21 seconds respectively. Further, the 2 trains cross each other in 24 seconds. Determine the ratio of the speed of the 2 trains?

Two trains running in opposite directions cross a stationary lady standing at point F in 26 seconds and 21 seconds respectively. The two trains cross each other in 24 seconds.

Let the speeds of Train 1 and Train 2 be $v_1$ and $v_2$ respectively.

Let the lengths of Train 1 and Train 2 be $L_1$ and $L_2$ respectively.

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When a train passes a stationary person, the train travels a distance equal to its own length.

For Train 1:

$L_1 = v_1 \times 26$

$L_1 = 26v_1$ ... (1)

For Train 2:

$L_2 = v_2 \times 21$

$L_2 = 21v_2$ ... (2)

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When the two trains cross each other while moving in opposite directions, their relative speed is $v_1 + v_2$.

The combined distance covered is $L_1 + L_2$ in 24 seconds.

$L_1 + L_2 = (v_1 + v_2) \times 24$ ... (3)

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Substituting (1) and (2) into (3):

$26v_1 + 21v_2 = 24(v_1 + v_2)$

$26v_1 + 21v_2 = 24v_1 + 24v_2$

$26v_1 - 24v_1 = 24v_2 - 21v_2$

$2v_1 = 3v_2$

$\dfrac{v_1}{v_2} = \dfrac{3}{2}$

Therefore, the ratio of the speeds of the two trains is $3:2$.