The current of stream runs at the rate of 4 km an hour. A boat goes 6 km and back to the starting point in 2 hours. The speed of the boat in still water is :
6 km/hr
7.5 km/hr
8 km/hr
6.8 km/hr
Explanation:
Let the speed of boat in still water be x km/hr
$\dfrac{6}{x+4}$+ $\dfrac{6}{x-4} $ = 2
=> $ 6 \left ( \dfrac{x-4+x+4}{(x+4)(x-4)} \right ) $ = 2
=> 6x = $x^{2}-16 $
=>$ x^{2}-6x-16 $ = 0
=>$ x^{2}-8x+2x-16 $= 0
=> x(x-8)+2(x-8) = 0
=> (x+2)(x-8) = 0
=> x = 8km/hr
Let the speed of boat in still water be x km/hr
$\dfrac{6}{x+4}$+ $\dfrac{6}{x-4} $ = 2
=> $ 6 \left ( \dfrac{x-4+x+4}{(x+4)(x-4)} \right ) $ = 2
=> 6x = $x^{2}-16 $
=>$ x^{2}-6x-16 $ = 0
=>$ x^{2}-8x+2x-16 $= 0
=> x(x-8)+2(x-8) = 0
=> (x+2)(x-8) = 0
=> x = 8km/hr