Question

A train travels 40 km at a uniform speed of $30km{h}^{-1}$. Its average speed after travelling another 40 km is $45km{h}^{-1}$ for the whole journey. Find its speed in the second half of the journey.

Answer 1

Let speed of the train in later half = x, then the time taken to travel later 40 km = 40/x hours ....[1 Mark]
Total time taken $=\frac{40}{30}+\frac{40}{x}$ .....[1 Mark]
Average speed = $\frac{Totaldistance}{Totaltime}=45$
$\frac{80}{\frac{40}{30}+\frac{40}{x}}=45$ .......[1 mark]
$4x+120=\frac{80}{45}\times 3x$
$x=90km{h}^{-1}$ ....[1 Mark]