Question

the speed of a boat in still water is 8 km per hour it can go up to 15 km upstream and 22 km downstream in 5 hours find the speed of the stream

Answer 1

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$\color{violet}{ \boxed{required \: answer}}$

Let the speed of the stream be x km/hr.

Given, speed of boat in still water = 8 km/h

Therefore, speed upstream = (8 – x) km/h

Speed downstream = (8 + x) km/h

Now, time taken by boat to go 22 km downstream 

=).
$\color{green}{ \boxed{ \frac{22}{x + 8}}}$

Time take by boat to go 15 km upstream
$\color{green}{ \boxed{\frac{15}{x - 8}}}$

Total time taken by boat = 5 hours.

∴ Time taken in downstream + Time taken in upstream = Total time taken by boat

$\color{green}{ \boxed{\frac{22}{8 + x} + \frac{15}{8 - x} = 5}}$

$\color{violet}{ \boxed{ {5x}^{2} - 7x - 320 + 296 = 0}}$

$\color{red}{ \boxed{ {5x}^{2} - 7x - 24 = 0}}$


$5x {}^{2} - 15x + 8x - 24 = 0$


$5x(x - 3) + 8(x - 3) \\ \\ (x - 3) = 0 \\ \\ x = 3$


∵ Speed of stream cannot be negative. Therefore, speed of stream is 3 km/h.