Question

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

Answer 1

Let the speed of sailor in still water be x km/hr and the speed of stream be y km/hr.

The speed of boat (upstream) = $(x-y)$ km/hr.

The speed of boat (downstream) =$(x+y)$ km/hr.

Now,

A.T.Q.

(1)$\frac{8}{x+y}=\frac{40}{60}$ (Since, Time = Distance / Speed)

===>$x+y=12$ ----------------- (1)

(2)$\frac{8}{x-y}=1$ (Since, Time = Distance / Speed)

===> $x-y=8$------------------- (2)

On adding (1) and (2),

===>$x+y+x-y=12+8$

===> $2x=20$

===>$x=10$

By (1),

===>$10+y=12$

===> $y=2$

Ans :- The speed of sailor in still water is 10 km / hr.

The speed of stream is 2 km / hr.