Question : 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/h, then the speed (in km/h) of the boat in still water is:
Option 1: 12
Option 2: 9
Option 3: 8
Option 4: 6
Correct Answer: 9
Solution :
Speed of the current, y = 3 km/h
Let the speed of the boat in still water be $x$ km/h.
According to the question,
$\frac{12}{x+3}+\frac{12}{x-3} =3$
⇒ $12(\frac{x-3+x+3}{(x+3)(x-3)})$ = 3
⇒ $4\times 2x = x^2 - 9$
⇒ $x^2 -8x-9 = 0$
⇒ $x^2-9x+x-9 = 0$
⇒ $x(x-9)+1(x-9) = 0$
⇒ $(x+1)(x-9) = 0$
We get two values of $x$ as –1 and 9.
The speed of the boat can not be –1.
Hence, the correct answer is 9 km/h.
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