Question

A boat takes 20 hours to travel 5 km upstream and 4 km downstream, but it takes 12 hours to travel 6 km upstream and 2 km downstream. Then speed of the boat in upstream is km/hr. ​

Answer 1

Answer:

20+5+4+12+6+2=49 is the answer

Answer 2

Given:

A boat takes 20 hours to travel 5 km upstream and 4 km downstream, but it takes 12 hours to travel 6 km upstream and 2 km downstream. Then speed of the boat upstream in km/hr?

​

To find:

The speed of the boat upstream in km/h

Solution:

Let,

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

"y" km/hr → Speed of the stream

So,

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

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

We know,

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

 

A boat takes 20 hours to travel 5 km upstream and 4 km downstream, so the equation will be:

$\frac{5}{x - y} + \frac{4}{x + y} = 20$  

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

$\implies 5u + 4v = 20$ . . . (1)

A boat takes 12 hours to travel 6 km upstream and 2 km downstream, so the equation will be:

$\frac{6}{x - y} + \frac{2}{x + y} = 12$  

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

$\implies 6u + 2v = 12$ . . . (2)

 

On multiplying eq. (1) by 2 and eq. (2) by 4, we get

10 u + 8v = 40 . . . (3)

24u + 8v = 48 . . . (4)

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

24u + 8v = 48

10u + 8v = 40

-       -       -

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

14u = 8

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∴ u = $\frac{8}{14}$

 

Therefore,

$\frac{1}{x - y} = u = \frac{8}{14}$

$\implies x - y = \frac{14}{8}$

$\implies x - y = \frac{7}{4}$  

$\implies \bold{x - y = 1.75 \:km/hr}$ ← speed upstream

 

Thus, the speed of the boat in upstream in km/hr is → 1.75 km/hr.

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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.

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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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