Problems on Trains Quiz Set 015

The trains cover a distance equal to the sum of their lengths at a relative speed 72 - 36 = 36km/h × (5/18), or 10m/s. We can use the speed distance formula: sum of lengths = 10 × 7 = 70m. Halving this we get the length of one train = 35m.

Let the normal speed be x km/hr. We have been given $12/x$ - $12/{x + 2}$ = 3. This translates to the quadratic equation $3x^2 + 6x - 24 = 0$, which can be solved to obtain x = 2 as the answer. If you don't want to solve the equation, then you can put each option into this equation and check that way. But this trick will work only if all the options have some numerical value.

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 ${107 + 45}/38$ = 4s.

The length of the train can be obtained from the time it takes to cross the pole. The length of the train = $18 × 16$ = 288m. To cross the platform it must travel a total distance equal to the combined lengths of the train and the platform at this speed. So time = ${288 + 864}/18$ = 64 seconds.

The distance to be covered is equal to the length of the train. This distance has to be covered at a net relative speed equal to the sums of the speeds of the jeep and the train, so v = 63 + 70 = 133. The length of the train will be time × speed = $8 × 133$ = 1064meters.