Question

Swati control board at a speed of 5 kilometre per hour in still water takes 1 hour more to Row the board 5.25 km upstream then to return downstream find the speed of the stream​

Answer 1

Answer:

The speed of stream is 2 km/h

Step-by-step explanation:

Given as :

Let The speed of stream = x km/h

Speed of boat in upstream = (5 -x) km/h

Speed of boat in down stream = (5 + x) km/h

Time taken to move 5.5 km upstream = $t_1$ = $\dfrac{5.5}{5 - x}$   hours

And , Time taken to move 5.5 km downstream = $t_2$ = $\dfrac{5.5}{5+x}$  hours

∵   $t_1$ = 1 + $t_2$

Or,  $\dfrac{5.5}{5 - x}$ =  1 +  $\dfrac{5.5}{5+x}$

Or, $\dfrac{5.5}{5 - x}$ - $\dfrac{5.5}{5+x}$ = 1

Or, 5.5 ( 5 + x) - 5.5 ( 5 - x) = (5 - x) (5 + x)

Or, 27.5 + 5.5 x - 27.5 + 5.5 x = 25 + 5 x - 5 x - x²

Or, 0 + 11 x = 25 + 0 - x²

Or, x ² + 11 x - 25 = 0

Now, Solving this quadratic equation

x = 1.9 ≈ 2  km/h

And x = - 12.9 ≈ - 13

So, The speed of stream = x = 2 km/h

Hence, The speed of stream is 2 km/h  Answer

Answer 2

Answer:

Let the speed of the stream be x km/h

Speed of boat upstream =(5-x) km/h

speed of boat downstream = (5+x) km/h

Distance travelled by boat in upstream=Distance travelled by boat in downstream=5.25 Km.

ATQ:-

→ 5.25(1/(5-x)-1/(5+x)=1.

→ 5.25 (2x/(25-x^2)=1.

→ 10.5x=25-x^2=0.

→ (x^2+10.5x-25=0.

→ (x+12.5)(x-2)=0.

→ x=2 Or x= -12.5

Speed can't be negative. So speed = 2 km/h