Question

A ship sails out to an island at the rate of 15 km/h and sails back to the starting point at 10 km/h. Find the average sailing speed for the whole journey.

Answer 1

Let the distance from the starting point to the island be x km.
Speed of the ship sailing out to the island = 15 km/h
Speed of the ship sailing back to the starting point = 10 km/h
We know:
$$\begin{gathered} \mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}} \\ \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{the}\mathrm{ship}\mathrm{to}\mathrm{travel}\mathrm{from}\mathrm{the}\mathrm{starting}\mathrm{point}\mathrm{to}\mathrm{the}\mathrm{island}=\frac{x}{15}\mathrm{h} \\ \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{the}\mathrm{ship}\mathrm{to}\mathrm{travel}\mathrm{from}\mathrm{the}\mathrm{island}\mathrm{to}\mathrm{the}\mathrm{starting}\mathrm{point}=\frac{x}{10}\mathrm{h} \\ \mathrm{Average}\mathrm{speed}=\frac{\mathrm{Total}\mathrm{distance}\mathrm{travelled}}{\mathrm{Total}\mathrm{time}\mathrm{taken}} \\ =\frac{x+x}{{\displaystyle \frac{x}{15}}+{\displaystyle \frac{x}{10}}} \\ =\frac{2x}{{\displaystyle \frac{2x+3x}{30}}} \\ =\frac{2x}{{\displaystyle \frac{5x}{30}}} \\ =\frac{60}{5} \\ =12\mathrm{km}/\mathrm{h} \end{gathered}$$

Therefore, the average speed of the ship in the whole journey was 12 km/h.