Question

A sailor goes 8 km downstream in 40 minutes and returns in 1 hour. Find the speed of the sailor in still water and the speed of the current.

Answer 1

Let the speed of the sailor in still water be x km/h and that of the current y km/h.
Speed downstream = (x + y) km/h
Speed upstream = (x − y) km/h
As per the question
$$\begin{gathered} \left(x+y\right)\times \frac{40}{60}=8 \\ \Rightarrow x+y=12.....\left(i\right) \end{gathered}$$
When the sailor goes upstream, then
$$\begin{gathered} \left(x-y\right)\times 1=8 \\ x-y=8.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$2x=20\Rightarrow x=10$
Putting x = 10 in (i), we have
$10+y=12\Rightarrow y=2$
Hence, the speeds of the sailor in staill water and the current are 10 km/h and 2 km/h respectively.