Problems on Trains Quiz Set 006

The trains cover a distance equal to the sum of their lengths at a relative speed 144 - 72 = 72km/h × (5/18), or 20m/s. We can use the speed distance formula: sum of lengths = 20 × 5 = 100m. Halving this we get the length of one train = 50m.

The total distance to be covered is equal to the length of the train plus the length of the tunnel. By the time and distance formula, we get time = distance/speed, which gives ${73 + 41}/57$ = 2s.

Let the speeds be v and 2v. The trains cover a distance equal to the sum of their lengths at a relative speed v + 2v = 3v. We can use the speed distance formula: $3v = {90 + 90}/6$, which gives v = ${180/{3 × 6}} × (18/5)$ = 36km/h. So the speed of the faster train is twice = 72km/h.

In 30 seconds the train covers a distance of 30 × 60 × (5/18) = 500 meters. This distance is the sum of the lengths of the train and the bridge. Subtracting the length of the train we get the length of the bridge = 500 - 129 = 371 meters.

The total distance is equal to the sum of the lengths of the trains, so s = 306. This distance has to be covered at a net relative speed equal to the difference of the speeds of the two trains, so v = 51. The time will be distance/speed = $306/51$ = 6s.