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A stream flows from A to B a distance of 30 km.at 2 km/hr and a man can row up and down in 8 hrs . Find the rate of the man in still water .
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Answer 1

Answer:

Brainly.in

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Secondary School Math 5 points

A stream flows from A to B a distance of 30 km at the rate of 2km/h and a man can row up and down in 8 hours.find the speed of the man in still watet.

Ask for details Follow Report by Huda1881 06.01.2019

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Me · Beginner

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hemangmehta63 Virtuoso

Answer:

8km/h

Step-by-step explanation:

Let the speed of man in still water be 'x'.

Distance = 30km

Speed of stream = 2km/h

Speed = Dist./Time

Time = Dist./speed

8hrs. = 30/x-2 + 30/x+2

8 = 30x + 60 + 30x - 60/x^2 - 4

8x^2 - 32 = 60x

0 = 8x^2 - 60x - 32

0 = 2x^2 - 15x - 8

0 = 2x^2 +x - 16x - 8

0 = x(2x + 1) - 8 (2x+1)

0 = (2x+1)(x-8)

x = -1/2 ; x = 8

As speed can't be negative,

x = 8km/h.

Answer 2

Answer:

Here is your answer

let

the rate of the man in still water = x km / hr

Relative rate of man down stream = ( x + 2 ) km / hr

Relative rate of man upstream = ( x + 2 ) km / hr

Distance from A to Be = 30 km

Time taken for the down journey = $\frac{30}{x~+~2}$ hrs

Time taken for the upward journey = $\frac{30}{x~-~2}$ hrs

Total time taken for both journeys = 8 hrs

→ $\frac{30}{x~+~2}{+}\frac{30}{x~-~2}$ = 8

→ $\frac{30 (x-2) + 30 (x+2)}{(x+2) (x-2)}$ = 8

→ $\frac{30x -60 + 30x + 60}{{x}^{2}{-}{4}}$ = 8

→ $\frac{60x}{{x}^{2}{-}{4}}$ = 8

→ ${8x}^{2}{-}{32}{=}{60x}$

→ ${8x}^{2}{-}{60x}{-}{32}{=}{0}$

→ ${2x}^{2}{-}{15x}{-}{8}{=}{0}$

→ ${2x}^{2}{-}{16x}{+}{x}{-}{8}{=}{0}$

2x ( x - 8 ) + 1 ( x - 8 ) = 0

( x - 8 ) ( 2x + 1 ) = 0

x - 8 = 0

:. $\huge\boxed{\fcolorbox{cyan}{yellow}{x~=~0}}$

2x + 1 = 0

2x = -1

x = - $\frac{1}{2}$

:. $\huge\bold{\fcolorbox{cyan}{red}{x~=~1/2}}$

The negative value of x is neglected

Hence

:.$\huge\boxed{\fcolorbox{cyan}{green}{x~=~8}}$

:. Rate or the man in still water = 8 km / hr .