Question

A boat travels 10 km upstream in the same amount of time it takes to travel
20 km downstream in the same river. If the speed of the river is 5 km/h, find
the speed of the boat in still water....pls answer on a paper I am very confused due to this question​

Answer 1

$\mathfrak{Hello!}$

$\text{Let the speed of the boat be (x - 5)}$

$\text{ n upstream and (x + 5) in downstream}</p><p>$

$s = \dfrac {d}{t}$

$\Rightarrow \dfrac {30}{5} = 6 hr$

$\Rightarrow \dfrac {50}{5} = 10 hr$

$\text{Then the equation will be}$

$6(x + 5) = 10(x - 5)$

$6x + 30 = 10x - 50$

$10x - 6x = 30 + 50$

$4x = 80$

$x = 20$

$\text{Speed of the boat in still water is 20km/hr}$

$\mathfrak{Thanks,\:please\:tell\:me\:if\:you\:have\:any\: questions}$

Answer 2

${\fbox{\boxed {\huge{\mathrm{\red{AnswEr}}}}}}$

Upstream = 10km

Downstream=20km

Speed of river (y) = 5 km/h

Speed of boat (x) = ?

We know that

${\star{\large{ \boxed{ \rm{ Speed = \frac{Distance}{Time}}}}}}$

Given time (t) is same for Upstream and Downstream

So ,

${\tt{\frac{10}{x - y} = \frac{20}{x + y}}}$

${\implies{\tt{10(x + y) = 20(x - y)}}}$

${\implies{\tt{10x + 10y) = (20x - 20y)}}}$

${\implies{\tt{10x - 20y) = (- 10x - 20y)}}}$

${\implies{\tt { - 10x = - 30y}}}$

${\boxed{ \implies{\tt {\blue{y = 5m/s}}}}}$

${\implies{\tt{- 10x = -30 \times 5}}}$

${\implies{\tt { \frac{30 \times 5}{10} }}} \\ {\implies{\tt { 3 \times 5 = 15 \frac{m}{s} }}}$

${\boxed {\huge{\green{\mathcal{BeBrainly}}}}}</p><p>$