Question

In a stream running at 2 kmph, a motor boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of the motor boat in still water.

Answer 1

Let the speed of the motor boat in still water be x kmph.

Speed downstream = (x+2) kmph

Speed upstream = (x-2) kmph

Therefore,

$\frac{10}{x-2}+\frac{10}{x+2}=\frac{55}{60}$

$\frac{1}{x-2}+\frac{1}{x+2}=\frac{55}{600}=\frac{11}{120}$

$11x^2-240x-44=0$

$(x-22)(11x+2)=0$

$x=22$

Therefore, speed of motor boat in still water = 22 kmph