On a 120 km long railway track, a train travels the first 80 km at a uniform speed of 160 km/h. What is the speed with which the train should move on the rest of the track so as to get the average speed of 80 km/h for the entire trip?

1 Answer
Sep 26, 2017

40(km)/h

Explanation:

Total length of Track =120km
break 120 km into two parts
a=80km and b=40km

While Travel First 80km=a
Speed v_a=160 (km)/h
Total Time taken to Travel path a is
t_a="distance"/"speed"=a/v_a=80/160=1/2 hr=30 min

Let the train travels at the speed of v_b while traveling on remaining track length of b=40km
Let time taken is t_b

Average Speed =("total distance")/("total time")
v_"avg"=(a+b)/(t_a+t_b)=120/(1/2+t_b)

But the Average speed for entire Trip is v_"avg"=80 (km)/(h)
Hence
80=120/(1/2+t_b)
=>1/2+t_b=120/80=3/2
t_b=3/2-1/2=1hr

time for travel last 40 km should be 1 hour
then the speed for rest of track length of 40 km is
v_b="distance"/"time"=40/1=40 (km)/h