Question

two trains 210m and 240m lon run on parallel tracks in the same direction.speed of the first train is 90m/hr and the second train crosses the first train in 36sec.find the time taken by them to cross in the opposite direction.

Answer 1

Task:

Two trains 210 m and 240 m long run on parallel tracks in the same direction. Speed of the first train is 90 miles/h and the second train crosses the first train in 36 s. Find the time taken by them to cross in the opposite direction.

Solution:

Find:

$t_2$

Given:

$s_1 - s_2 = 30\ m = 0.019\ miles$

$$v_1 = \text{const} = 90\ \frac{\text{miles}}{\text{hour}}$$ $$v_2 = \text{const}$$ $$t = 36\ s = 0.01\ \text{hour}$$ $$s_1 = v_1 \cdot t = 0.9\ \text{miles}$$ $$s_2 = v_2 \cdot t$$ $$s_2 = s_1 - 0.019\ \text{miles}$$ $$v_2 = \frac{s_2}{t} = \frac{s_1 - 0.019\ \text{miles}}{t} = 88.136\ \frac{\text{miles}}{\text{hour}}$$

Since we don't know the initial distance between the trains when they move in the opposite direction (suppose that the initial distance between them in the opposite direction equals

$s_1 - s_2 = 30\ m = 0.019\ \text{miles}$):

$$v_1 \cdot t_2 + v_2 \cdot t_2 = 0.019\ \text{miles}$$ $$t_2 = \frac{0.019\ \text{miles}}{v_1 + v_2} = 0.384\ s$$

Answer:

$t_2 = 0.384\ s$