Question

a train travels the first 30 km of 120 km track with a uniform speed of 30 km/hr. what should be the speed of the train to cover the remaining distance of track so its average speed is 60 km/hr for the trip.

Answer 1

if v1 is initial velocity and v2 is final velocity
then average velocity(v) =2.v1.v2/v1+v2
=>60=30.v2/30+v2
=>v2=60km/hr
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Answer 2

Distance already covered = 30 km
So the distance to be covered =120-30 =90 km

Time taken to cover first 30 km = 30/30 = 1 hr

Let the speed be x km/hr
Then time taken to complete 90 km = 90/x hr

Average velocity = Total distance / Total time
= 120 / (90/x + 1) and we know that average velocity = 60 km/hr

So, 120/(90/× + 1) = 60
=> 120x / (90 + x) = 60
=> 120x = 60 (90 + x)
=> 120x = 5400 + 60x
=> 60x = 5400
=> x = 90

So the train should travel at 90 km/hr