Question

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?

Answer 1

`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`