Problems on Trains Quiz Set 010

The speed of the train in m/s is 18 × (5/18) = 5 m/s. The length of the train can be obtained from the time it takes to cross the man = $5 × 9$ = 45meters. The combined length of the train and platform can be obtained from the time it takes to cross the platform, = $5 × 45 = 225$ meters. Subtracting, we get the length of the platform= 180 m.

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. By the time and distance formula, we get time = distance/speed, which gives $656/82$ = 8s.

Let the ratio of their speeds by r. If the speed of one train is v, then the speed of the other is rv. By the speed and distance formula, the sum of their lengths is $(v × 16) + (rv × 69)$ which should equal the value obtained from the time they take to cross each other,i.e., $(v + rv) × 32)$. So $v × (16 + r × 69$ = $v × (1 + r) × 32).$ Cancelling v and solving for r we get ${16/37}$.

The total distance to be covered is equal to the length of the train. By the time and distance formula, we get time = distance/speed, which gives $315/45$ = 7s.