On a straight 60 km track, a train travels the first 30 km with a uniform speed of 30 km/hr. How  fast must the train travels for remaining 30 km so that average speed is 40 km/hr for the entire trip?

here by the question,S1=S2=30kmS=60 kmv1=30km/hrvavg=40 km/hrv2=?But average speed=vavg=total distancetotal time=S1+S2t1+t2 vavg=S+SSv1+sv2 vavg=2SS1v1+1v2 vavg=2v1v2v1+v2 substitute given values, 40=2×30×v230+v2 ⇒30+v2=32v2 ⇒v2=60 km/hr