Question

a boat travel 16km upstream and 24km downstream in 6 hours.
The same boat travel 36 km upstream 48 km downstream in 13 hours
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Answer 1

Answer:

Speed of Boat in still water $\longrightarrow$ 8km/h.

Speed of the stream $\longrightarrow$ 4km/h.

Correction in the Question:

A boat travels 16km upstream and 24km downstream in 6 hours.  The same boat travel 36 km upstream 48 km downstream in 13 hours . Find the speed of the boat in still water and the speed of the stream.

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Step-by-step explanation:

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

Let the speed of the stream by 'y'.

Upstream $\longrightarrow$ Going against the flow of water.

Downstream $\longrightarrow$ Going with the flow of water.

Since when Flowing Upstream, the object floating floats against the flow of water, the equation is negative.

Since when Flowing Downstream, the object floating floats with the flow of water, the equation is positive.

$\large\boxed{\sf\therefore Upstream = \frac{1}{x \ - \ y}}$ and $\large\boxed{\sf\therefore Downstream = \frac{1}{x \ + \ y}}$

According to the question,

$\sf\dfrac{16}{x \ - \ y} + \dfrac{24}{x \ + \ y} = 6$

$\sf\dfrac{36}{x \ - \ y} + \dfrac{48}{x \ + \ y} = 13$

Let us take that,

$\large\boxed{\sf{\dfrac{1}{x \ - \ y} = a}}$

$\large\boxed{\sf{\dfrac{1}{x \ + \ y} = b}}$

Substituting the values of 1/x - y and 1/x + y in the equations formed.

16a + 24b = 6 .......(1)

36a + 48b = 13 ........(2)

Multiplying equation (1) by 2 we get ↓

32a + 48b = 12 ..........(3)

Subtracting equation (2) by (3)

36a + 48b = 13

(-)    (-)       (-)

32a + 48b = 12

____________

4a = 1

$\large\boxed{\sf\therefore a = \dfrac{1}{4}}$

Substituting 'a' in equation number (1)

16a + 24b = 6 .......(1)

16$\sf[\frac{1}{4}]$ + 24b = 6

4 + 24b = 6

24b = 6 - 4

24b = 2

$\sf b = \frac{2}{24}$

$\large\boxed{\sf\therefore b = \dfrac{1}{12}}$

Now Equate the values of,

$\longrightarrow \sf \ 'a' \ with \ \frac{1}{x \ - \ y}$

$\longrightarrow \sf \ 'b' \ with \ \frac{1}{x \ + \ y}$

Value of 'x - y':

$\large\boxed{\sf{\dfrac{1}{x \ - \ y} = a}}$

$\sf\dfrac{1}{x \ - \ y} = \dfrac{1}{4}$

$\large\boxed{\sf\ x \ - \ y = 4}$ ......(4)

Value of 'x + y':

$\large\boxed{\sf{\dfrac{1}{x \ + \ y} = b}}$

$\sf\dfrac{1}{x \ + \ y} = \dfrac{1}{12}$

$\large\boxed{\sf\ x \ + \ y = 12}$ ......(5)

Adding equation (4) and (5) we get,

x + y = 12

x - y = 4

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2x = 16

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

x = 8 km/h.

Substitute the value of 'x' in equation (5)

x + y = 12

8 + y = 12

y = 12 - 8

y = 4 km/h.

∴ The speed of the boat in still water is 8km/h.

∴ The speed of the stream is 4km/h.

Answer 2

Answer:

Speed still in water is 8 km/hr

Step-by-step explanation:

speed in the stream is 4 km/hr