Question

A boat running downstream, covers a distance of 20 km in 2 h, while it covers the same distance upstream in 5 h. then, speed of the boat in still water is

Answer 1

Let, the speed of the boat be u km/h in still water.
let the speed of the stream be v km/h.

While going upstream-

$\dfrac{20}{u - v} = 5$ ...... (1)

While going downstream-

$\dfrac{20}{u + v} = 2$ ...... (2)

Now, from (1),
$u - v = \frac{20}{5}$
or, $u - v = 4$
or, $u = v + 4$ ..... (3)

Now, from (2),
$\dfrac{20}{v + 4 + v} = 2$
or, $\dfrac{20}{2(v+2)} = 2$
or, $\dfrac{10}{v + 2} = 2$
or, $v + 2 = \frac{10}{2}$
or, $v = 5 - 2$
or, v = 3 km/h

from (3),
u = 3 + 4 = 7 km/h

Hence, the speed of the boat in still water is 7 km/h.