# It took a crew 2 hours 40 minutes to row 6 km upstream and back again. If the rate of flow of the stream was 3 km/h, what was the rowing speed of the crew in still water?

May 30, 2018

Rowing speed in steel water is $6$ km/ hour.

#### Explanation:

Let the rowing speed in steel water be $x$ km/ hour

Rowing speed in upstream is $x - 3$ km/ hour

Rowing speed in downstream is $x + 3$ km/ hour

Total time taken is $2$ hrs $40$ minutes i.e $2 \frac{2}{3}$hour

to cover up and down journey of $12$ Km

$\therefore \frac{6}{x - 3} + \frac{6}{x + 3} = \frac{8}{3}$ Multiplying by $3 \left({x}^{2} - 9\right)$ on both

sides we get, $18 \left(x + 3\right) + 18 \left(x - 3\right) = 8 \left({x}^{2} - 9\right)$ or

$8 {x}^{2} - 36 x - 72 = 0 \mathmr{and} 2 {x}^{2} - 9 x - 18 = 0$ or

$2 {x}^{2} - 12 x + 3 x - 18 = 0$ or

$2 x \left(x - 6\right) + 3 \left(x - 6\right) = 0 \mathmr{and} \left(2 x + 3\right) \left(x - 6\right) = 0$

:.x= 6 or x =-3/2 ; x != -3/2 :. x =6 km/hr

Rowing speed in steel water is 6 km/ hour [Ans]