Problems on Trains Quiz Set 003

Let the speed of the train be v km/h. Distance travelled by this train in (7 + 21) hours = 28v km. Equating this to the distance travelled by the second train we get 28v = 4 × 7, which gives v = 1 km/h.

The trains cover a distance equal to the sum of their lengths at a relative speed 24 + 48 = 72km/h × (5/18), or 20m/s. We can use the speed distance formula: sum of lengths = 20 × 11 = 220m. Halving this we get the length of one train = 110m.

The total distance to be covered is equal to the length of the train. By the time and distance formula, we get length = time × speed, which gives $3 × 56$ = 168m.

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 $(v × 14) + (rv × 42)$ which should equal the value obtained from the time they take to cross each other,i.e., $(v + rv) × 31)$. So $v × (14 + r × 42$ = $v × (1 + r) × 31).$ Cancelling v and solving for r we get ${17/11}$.

The total distance to be covered is equal to the length of the train. By the time and distance formula, we get length = time × speed × (5/18), which gives $36 × 82 × (5/18)$ = 820m. Please note that 5/18 is the conversion from km/h to m/s.