Question

Solve please..... .........fast

Answer 1

Hello friend

Here is your answer!!!!!!!

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Ans==>>

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

Therefore,

the speed of the boat downstream
= (x + y) km/hr

and
the speed of the boat upstream= (x - y) km/hr

Now,we know that,

$time = \frac{distance}{speed}$

Therefore, time taken by the boat to cover 16km upstream =

$\frac{16}{x - y} \: hours$

and the time taken by the boat to cover 24 km downstream =

$\frac{24}{x + y} \: hours$

But, the total time taken by the boat to cover 16km/hr upstream and 24 km downstream is 6 hours.

:
$\frac{16}{x - y} + \frac{24}{x + y} = 6 \: \: ..........(1)$

Similarly,by the second condition,

:
$\frac{36}{x - y} + \frac{48}{x + y} = 13 \: \: ............(2)$

$substituting \: \frac{1}{x - y} = 1 \: and \: \: \frac{1}{x + y} = b \\ in \: equation \: (1) \: and \: (2)$

16a + 24b = 6 ..................(3)

36a + 48b = 13 ...................(4)

Multiplying equation (3) by 2 we get,

32a + 48b = 12 .....................(5)

Subtracting equation (5) from equation (4) we get,

36a + 48b = 13

32a + 48b = 12
----------------------------

4a = 1

$a = \frac{1}{4}$

Substituting the value of a in equation (3) we get,

$16 \times \frac{1}{4} + 24b = 6 \\ \\ 4 + 24b = 6 \\ \\ b = \frac{1}{12}$

Resubstituting the values of a and b we get,

$\frac{1}{x - y} = \frac{1}{4} \: and \: \frac{1}{x + y} = \frac{1}{12}$

: x - y = 4 ......................(6)

and x + y = 12 ..................(7)

Adding equation (6) and (7) we get,

x - y = 4

x + y = 12
----------------

2x = 16

$x = \frac{16}{2} \\ \\ x = 8$

Substituting the value of x in equation (7)

x + y = 12

8 + y = 12

y = 12 - 8

y = 4

Therefore,the speed of the boat in still water is 8 km/hr

and

The speed of the stream is 4km/hr.

Thanks...

:)