On a 60km track, a train travels the first 30km with a speed of 30kmh−1 . How fast must the train travel the next 30km so as to average 40kmh−1 for the whole trip?

 It is given that the first 30km is traveled with the speed 30kmh−1 , let us consider that the speed with which the next 30km is travelled be xkmh−1

Now as we know that time=distance/speed

This implies the time t1 taken to travel the first 30km will be

t1 = 30km/30kmh−1 = 1h

The time taken to travel the next 30km will be

t2=30km/xkmh−1 = 30/x h

Now as the average speed for the whole trip is 40kmh−1 , so, average time taken for whole trip is

t = 60km/40kmh−1 = 3/2h

This implies 1h+30/x h = 3/2h

Further solving for the value of x ,

we get ⇒ 30/x = 1/2

⇒ x = 60 Thus, the train travels the next 30km with the speed 60kmh−1