Question

the distance between delhi and ambala is 200 km. A train travels 100km at a speed of 50km/hr. How fast the train must travel so as to average speed is 70km/hr?

Answer 1

Total distance to be covered by the train = 200 km.
Speed of the train while covering 100 km = 50 km/hr.
Average speed of the train should be 70 km/hr.
Let the train cover the rest of the distance i.e. (200-100) km = 100 km with a speed of N km/hr.
We know that Speed = Distance/Time.
So, Time = Distance/Speed. Now, average time taken by the train will be sum of the time taken by the train while travelling with speed of 50 km/hr and N km/hr.
Therefore, 200/70 = 100/50 + 100/N or, 200/70 = (2N + 100)/N or, 200N = 140 N + 7000 or, 60 N = 7000 or, N = 7000/60 =116.67 km/hr = 117 km/hr. Thus, the train should travel the last 100 km with a speed of 117 km/hr.