Question

Example 19: A boat goes 30 kmupstream and 44 km downstream in
10 hours. In 13 hours, it can go
40 km upstream and 55 km
down-stream. Determine the speedof the stream and that of the boat instill water.​

Answer 1

Let the speed of boat in still water be xkm/h

and speed of stream be ykm/h

While going upstream

speed=(x-y)km/h

Distance=30km

$\rm time = \frac{distance}{speed} \\ \rm { time = \frac{30}{x - y} }$

We have to take t1 as it is difficult to seperate time of downstream and upstream

$\rm \boxed{ t_{1} = \frac{30}{x - y} }$

While going downstream

speed=(x+y)km/h

distance=44km

$\rm time = \frac{distance}{speed} \\ \rm \boxed{t_{2} = \frac{44}{x + y} }$

We have total time so we add t1 and t2 equation

$\rm 10 = \frac{30}{x - y} + \frac{44}{x + y} \\ \rm let \frac{1}{x - y} \: be \: u \: and \: \frac{1}{x + y} \:be \: v \\ \implies \boxed{30u + 44v = 10 }$

Similarly we do 2nd equation which is In 13 hours, it can go 40 km upstream and 55 km

down-stream

$\rm \implies \boxed{40u + 55v = 13}$

We can use elimination method for solving that equation

$\rm 30u + 44v = 10 \\ \rm 40u + 55v = 13$

Now multiply 4 in 1st and 3 in 2nd as you know about elimination method

$\rm \: \: \: \: \: 120u + 176v = 40 \\ \rm \boxed{ - }120u + 165v = 39 \\ - - - - - - - - - - \\ \rm 11v = 1 \implies \boxed{v = \frac{1}{11} and \: u = \frac{1}{5} }$

Now put orginal value question isn't ended yet

$\rm \implies\frac{1}{x - y} = \frac{1}{11} \implies \boxed{x - y = 5}$

and

$\rm \frac{1}{x + y} = \frac{1}{11} \implies \boxed{x + y = 11}$

Using elimination once again

$\rm \: \: \: \: x - y = 5\\ \rm \boxed{ - }x + y = 11 \\ - - - - - - - \\ \rm \boxed{y = 3} \:and \boxed{x = 8}$

Answer 2

Answer:

Y = 3

And

X= 8

Step-by-step explanation:

Hope you understood

Pls mark as brainlist

Also pls thanks if it helps