Q. The current of a stream runs at the rate of 4 km an hour. A boat goes 6 km and comes back to the starting point in 2 hours. The speed of the boat in still water is :
Answer: 8 km/hr
Notes: Let the speed of boat in still water be x km/hr. $latex \therefore \frac{6}{x+4}+\frac{6}{x-4} = 2&s=1$ $latex => 6\left ( \frac{x-4+x+4}{(x+4)(x-4)} \right ) = 2&s=1$ $latex => 6x = x^{2}-16$ $latex => x^{2}-6x-16 = 0$ $latex => x^{2}-8x+2x-16 = 0$ $latex => x(x-8)+2(x-8) = 0$ $latex => (x+2)(x-8) = 0$ $latex => x = 8km/hr$ Hence option [D] is correct answer.