Question

A Boat goes 30 km upstream and 44 km downstream in 10 hours in 13 hours it can go 40 kilometre upstream and 55 km downstream find the speed of the stream and that of the boat in still water solve by elimination method

Answer 1

Let the speed of the the boat is xkm/hr.

Let the speed of the stream be ykm/hr.

(i)

Given that boat goes 30 km upstream and 44 kms downstream in 10 hours.

Speed upstream + Speed downstream = Time taken

⇒ (30/x - y) + (44/x + y) = 10

Let x - y = u and x + y = v.

⇒ 30u + 44v = 10

(ii)

Given that it can go 40km upstream and 55km downstream in 13 hours.

⇒ (40/x - y) + (55/x + y) = 13

Let x - y = 40 = u and x + y = v.

⇒ 40u + 55v = 13.

Elimination Method:

On solving (i) *4 & (ii) * 3, we get

⇒ 120u + 176v = 40

⇒ 120u + 165v = 39

   ------------------------

                11v = 1

                  v = 1/11

Then, x + y = 11.   ----- (iii)

Substitute v = (1/11) in above equations, we get

⇒ 120u + 176v = 40

⇒ 120u + 176(1/11) = 40

⇒ 120u + 16 = 40

⇒ 120u = 24

⇒ u = (1/5).

Then, x - y = 5.    ----- (iv)

Now,

On solving (iii) & (iv), we get

⇒  x + y = 11

⇒ x - y = 5

   ----------------

    2x = 16

       x = 8

Substitute x = 8 in (iv), we get

⇒ x - y = 5

⇒ 8 - y = 5

⇒ y  = 3.

Therefore:

⇒ Speed of the boat = 8 km/hr.

⇒ Speed of stream = 3 km/hr.

Hope it helps!

Answer 2

A boat going upstream is represented by x-y

A boat going downstream is represented by x+y

Formula of speed: $s = \frac{d}{t}$

set-up the system of equations

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

Use above to transfigure the equation pertaining to the 13hour trip

30u + 44d = 10

40u + 55d = 13

u = 1/5 d= 1/11

1/5= 1/x-y 1/11= 1/x+y

x: speed of boat still in water

y: speed of stream

x-y= 5 x+y= 11

substitue

x = y + 5

y + 5 + y = 11

2y + 5 = 11

y = 3

x + 3 =11

x = 8

x = 8

y = 3

Answer

$\boxed {8\text{ km/hr} = \text {speed of boat still in water}}$

$\boxed {3\text{ km/hr} = \text {speed of stream}}$