Q. A boat goes 12 km downstream and comes back to the starting point in 3 hours. If the speed of the current is 3 km/hr, then the speed (in km/hr) of the boat in still water is :
Answer: 9
Notes: Let the speed of boat in still water be x km/hr then,
$latex \frac{12}{x+3}+\frac{12}{x-3} = 3&s=1$
$latex => 12\left ( \frac{x-3+x+3}{(x+3)(x-3)} \right ) = 3&s=1$
$latex => 4\times 2x = x^{2}-9$
$latex => x^{2}-8x-9 = 0$
$latex => x^{2}-9x+x-9 = 0$
$latex => x(x-9)+1(x-9) = 0$
$latex => (x-9)(x+1) = 0$
$latex => x = 9, x\neq -1.$ Because speed cannot be negative.
Hence speed of boat in still water is 9 km/hr.
Hence option [C] is correct answer.
