Question

on a 120 km track a train travels the first 30 kms at a uniform speed of 30 km/hr. calculate the speed with wch the train should move rest of the track so as to average 60 km/hr for the entire trip

Answer 1

distance here is 120km.
we can take first 30 km as d1 and next 90 as d2.
Average speed is total distance /total time
part 1: d1=30km
           s1=30km/h
            t1=1h
part2:
            d2=90km
           s1=(let it be x) x
           t2=90/x
Now,average speed=total distance/total time
60=120/(1+90/x)
    =120/(x+90/x)
    =120x/90+x
60(90+x)=120x
4800+60x=120x
4800=120x-60x
4800=60x
x=4800/60
x=80km/h

Answer 2

                           ANSWER                            

                          In the first 30 km speed of the train, v1 = 30 km/h

                          Speed of the train in the next 90 km, v2 (to be determined)

                         Average speed = 60 km/h = (v1 + v2)/2  

                                         = (30 km/h + v2)/2  

                              → v2 = 90 km/h