Swati control board at a speed of 5 kilometre per hour in still water

1.	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» 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

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»

Answer:

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