Question

Two trains are moving with equal speed in opposite directions along two parallel tracks. If the wind is blowing with speed u along the track so that the relative velocities of the trains with respect to the wind are in the ratio 1:2, then the speed of each train must be:

a) u
b) 2u
c) 3u
d) 4u

Answer 1

The speed of each train can be determined by considering the relative velocities with respect to the wind. The speed of each train is 3 times the speed of the wind (3u).

Step-by-step explanation:

The speed of each train can be determined by considering the relative velocities with respect to the wind. Let's assume that the speed of each train is 'v'.

The relative velocity of the first train with respect to the wind is (v + u) and the relative velocity of the second train with respect to the wind is (v - u). According to the given information, these relative velocities are in the ratio 1:2. Therefore, we can write the equation (v + u) / (v - u) = 1/2.

Simplifying this equation, we get 2(v + u) = v - u.

Solving for 'v', we find that v = 3u.

Thus, the speed of each train is 3 times the speed of the wind (3u).