Question

The boat sailed 24 km down the river and 15 km along the river in 3 hours, and 8 km down the river and 35 km along the river in 4 hours. How fast is the boat sailing on calm water?​

Answer 1

Given:

The boat sailed 24 km down the river and 15 km along the river in 3 hours, and 8 km down the river and 35 km along the river in 4 hours. How fast is the boat sailing on calm water?

To find:

How fast is the boat sailing on calm water?

Solution:

Let,

"x" km/hr → Speed of the boat in still water

"y" km/hr → Speed of the stream

So,

Speed upstream = (x - y) km/hr

Speed downstream = (x + y) km/hr

We know,

$\boxed{\bold{Time = \frac{Distance}{Speed} }}$

 

The boat sailed 24 km down the river and 15 km along the river in 3 hours, so the equation will be:

$\frac{24}{x + y} + \frac{15}{x - y} = 3$  

taking $\frac{1}{x+ y} = v \:and \:\frac{1}{x-y} = u$

$\implies 24v + 15u = 3$ . . . (1)

The boat sailed 8 km down the river and 35 km along the river in 4 hours, so the equation will be:

$\frac{8}{x + y} + \frac{35}{x - y} = 4$  

taking $\frac{1}{x+ y} = v \:and \:\frac{1}{x-y} = u$

$\implies 8v + 35u = 4$ . . . (2)

On multiplying equation (1) by 8 and equation (2) by 24, we get

$192v + 120u = 24$ . . . (3)

$192v + 840u = 96$ . . . (4)

On subtracting equations (3) and (4), we get

192v + 120u = 24

192v + 840u = 96

-       -               -

-----------------------------

         - 720u = - 72

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∴ u = $\frac{1}{10}$

 

On substituting the value of u in equation (1), we get

$\implies 24v + \frac{15}{10} = 3$

$\implies 24v = 3 - \frac{3}{2}$

$\implies 24v = \frac{3}{2}$

$\implies v = \frac{1}{16}$

Therefore,

$\frac{1}{x+y} = v = \frac{1}{16}$

$\implies x + y = 16$ . . . (5)

and

$\frac{1}{x-y} = u = \frac{1}{10}$

$\implies x - y = 10$ . . . (6)

On adding equations (5) and (6), we get

x + y = 16

x - y = 10

---------------

2x = 26

----------------

∴ x = 13 km/hr ← speed of the boat in the still water

Thus, the boat is sailing at a speed of 13 km/hr on the calm water.

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Also View:

A person can row 50 kms upstream and 70 kms downstream in 4 hours. He can row 35 kms downstream and 75kms upstream in 4 hours. Find the speed of the person in still water and the speed of the current.

brainly.in/question/4874410

A boatman rows his boat 35 km upstream and 55 km downstream in 12 hours. he can row 30 km. upstream and 44 km downstream in 10 hours. find the speed of the stream and that of the boat in still water. hence find the total time taken by the boatman to row 50 cm upstream and 77 km downstream

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Answer 2

it is only the answer you understand