Question

a person rowing at the rate of 5km/h in still water , takes as much time as in going 40 km upstream as in 40 km downstream . Find the speed of stream​

Answer 1

Answer:

Appropriate Question :-

• A person rowing at the rate of 5 km/h in still water, take thrice as much as time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

Given :-

• A person rowing at the rate of 5 km/h in still water, take thrice as much as time in going 40 km upstream as in going 40 km downstream.

To Find :-

• What is the speed of the stream.

Solution :-

Let,

$\mapsto \bf Speed\: of\: the\: stream =\: x\: km/h$

$\bigstar$ Speed of the boat in still water is 5 km/h.

Then,

$\leadsto \sf Speed\: of\: the\: boat\: upstream =\: (5 - x)\: km/h$

$\leadsto \sf Speed\: of\: the\: boat\: downstream =\: (5 + x)\: km/h$

According to the question,

$\implies \sf \dfrac{40}{(5 - x)} =\: 3\bigg\lgroup \dfrac{40}{(5 + x)}\bigg\rgroup$

$\implies \sf \dfrac{40}{(5 - x)} =\: \dfrac{120}{(5 + x)}$

By doing cross multiplication we get,

$\implies \sf 120(5 - x) =\: 40(5 + x)$

$\implies \sf 600 - 120x =\: 200 + 40x$

$\implies \sf - 120x - 40x =\: 200 - 600$

$\implies \sf {\cancel{-}} 160x =\: {\cancel{-}} 400$

$\implies \sf 160x =\: 400$

$\implies \sf x =\: \dfrac{40\cancel{0}}{16\cancel{0}}$

$\implies \sf x =\: \dfrac{40}{16}$

$\implies \sf\bold{\red{x =\: 2.5\: km/h}}$

${\small{\bold{\underline{\therefore\: The\: speed\: of\: the\: stream\: is\: 2.5\: km/h\: .}}}}$