Question

On a 120 km track, a train travels the first 30 km at a uniform speed of 30 km/h. Calculate the speed with which the train should move rest of the track so as to get the average speed of 60 km/h for the entire trip?

Answer 1

Dear student

$$\begin{gathered} timetakenforthefirst30km=\frac{dis\tan ce}{speed}=\frac{30}{30}=1hour \\ restdis\tan cetocover=120-30=90km \\ letspeedtocover90kmisvkm/hraveragevelocity \\ {V}_{average}=\frac{totaldis\tan ce}{totaltime}=\frac{120}{1+{\displaystyle \frac{90}{v}}} \\ 60=\frac{120}{1+{\displaystyle \frac{90}{v}}} \\ 1+\frac{90}{v}=\frac{120}{60}=2 \\ \frac{90}{v}=2-1=1 \\ \frac{90}{v}=1 \\ v=90km/hr \\ Regards \end{gathered}$$