Answer to Question #79277 in Mechanics | Relativity for Hrutil Tandel

Question #79277

Two trains A and B each of length 100m, are moving with their constant speeds.If one train A overtakes the other in 40s and cross the other in 20s. Find speed of each trains.

Expert's answer

Let vA and vB be a velocity of two trains A and B. While overtaking the velocity of train A relative to train B is vA - vB m/s.
While overtaking or crossing, the trains have to cover a total distance of 100 + 100 = 200 m.
Then using the formula Distance = Speed * Time, we can write
(vA - vB)*40 = 200 m (1)
In case of crossing the velocity of train A relative to train B is vA + vB m/s. The total distance is the same and equal 200 m. Then
(vA + vB)*20 = 200 m (2)
Let's solve equations 1 and 2.
(vA - vB) = 200/40 = 5,
(vA + vB) = 200/20 = 10,
vA = vB + 5,
vB + 5 + vB = 10,
2vB = 5,
vB = 5/2 = 2.5 m/s,
vA = 2.5 + 5 = 7.5 m/s.