Question

A train travels 40 km at a uniform speed of 30 km h".lts average speed after travelling another 40km Is 45 km h" for the whole Journey. Find its speed of “the second half of the journey.

Answer 1

$$\begin{gathered} \mathrm{Average}\mathrm{speed}: \\ \mathrm{v}=\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Total}\mathrm{time}} \\ 45=\frac{40+40}{{\displaystyle \frac{40}{30}}+{\displaystyle \frac{40}{\mathrm{x}}}} \\ \frac{40}{30}+\frac{40}{\mathrm{x}}=\frac{80}{45} \\ \frac{40}{\mathrm{x}}=\frac{80}{45}-\frac{40}{30} \\ \frac{40}{\mathrm{x}}=\frac{16}{9}-\frac{4}{3} \\ \frac{40}{\mathrm{x}}=\frac{16}{9}-\frac{12}{9} \\ \frac{40}{\mathrm{x}}=\frac{4}{9} \\ 4\mathrm{x}=360 \\ \mathbf{x}\mathbf{=}\mathbf{90}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{h} \end{gathered}$$