Question

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can
go 40 km upstream and 55 km downstream. Determine the speed of the stream and
that of the boat in still water.
​

Answer 1

Step-by-step explanation:

When the boat down the speed inrease and and when it down up the speed decrease.

Speed = Distance / time

ATQ

30/x-y + 44/x+y = 10 ----- 1

40/x-y + 55/x+y = 13----- 2

let 1/x-y be a and 1/x+y be b

30a + 44b = 10

40a + 55b = 13

Then apply elimination in both equation and u will get ur answer..

40(30a+44b)= 10

30(40a + 55b ) = 13

Then solve ahead so simple.. ahead portion is.. Hope it will help u .. and if u have any problem in the ahead part let me know on my I'd of brainly.. ask me on that

Answer 2

Given:- A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can

go 40 km upstream and 55 km downstream. Determine the speed of the stream and

that of the boat in still water.

Solution:-

Let the speed of a boat in still water be X Km/h and speed of the stream be Y Km/h.

Speed upstream = ( X - Y ) Km/h

Speed downstream = ( X + Y ) Km/h.

Let,

$\frac{1}{x - y} = a \: and \frac{1}{x + y} = b$

$= \frac{30}{x - y} + \frac{44}{x + y} = 10$

⭐ 30A + 44B = 10

⭐ 120A + 176B = 40

$= \frac{40}{x - y} + \frac{55}{x + y} = 13$

⭐ 40A + 55B = 13

⭐ 120A + 165B = 39

On subtracting eqn ( 1 ) - eqn ( 2 ) We get :-

120A + 176B - 120A - 165B = 40 - 39

$b = \frac{1}{11}$

⭐ 30A + 4 = 10

⭐ 30A = 6

$= a = \frac{6}{30} = \frac{1}{5}$

⭐ X - Y = 5 and X + Y = 11

X + Y + X - Y = 5 + 11 = 16

⭐ 2X = 16 or X

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

Substitute X = 8 in X + Y = 11

We get :- Y = 11 - X = 11 - 8 = 13

⭐ X = 8, Y = 3

Speed of a boat in still water = 8 Km/h

and speed of stream = 13 Km/h.

$\huge \boxed {\fcolorbox{red}{blue}{solved}}$