on a 60km track,a train travels the first 30 km with a uniform speed of 30km/h. How fast must the train travel the next 30km so as to average 40km/h for the entire trip? please explain briefly.

Time taken for first interval: t1 = 30/30 = 1 hr

average speed to maintain: v = 40 km/hr

total distance, s = 60 km.

Since average speed = (total distance travelled)/(total time taken)

thus total time taken: T =  60/40 = 3/2= 1.5 hr

thus time taken for second interval = 0.5 hr

thus speed in second interval: 30/0.5 = 60 km/hr