On a 120km/h track ,a train travels the first 30km at a uniform speed of 30km/h .how fast must the train travel the next 90 km somas to average 60km/h for the entire trip?
Total distance covered, S = 120 km
First 30 km is covered at 30 km/h.
Time taken is, t 1 = 30/30 = 1 hour
Let the train covers next 90 km at speed x km/h.
Then the time taken is, t 2 = 90/x hour
Average speed = total distance/total time
=> 60 = 120/(t 1 + t 2 )
=> 60 = 120/(1 + 90/x)
=> 1 + 90/x = 2
=> 90/x = 1
=> x = 90 km/h
Thus, to achieve an average speed of 60 km/h the train must travel the next 90 km at 90 km/h.