Question

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

• A. 6 km/hr
• B. 8 km/hr
• C. 7.5 km/hr
• D. 6.8 km/hr

Answer 1

Answer:

B. 8 km/hr

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

$\frac{6}{x+4}+\frac{6}{x-4}=2$

$6[\frac{x-4+x+4}{x^2-4^2}]=2$

$\frac{2x}{x^2-16}=\frac{2}{6}$

$6x=x^2-16$

$x^2-6x-16=0$

$x^2-8x+2x-16=0$

$x(x-8)+2(x-8)=0$

$(x-8)(x+2)=0$

$x=8,X=-2$

Value can't be negative

So speed of Boat in Still water is 8 kmph.