Question : A boat takes a total of 2 hours to cover 9 km downstream and return, given that the speed of the stream is 6 km/hr. What is the speed of the boat in still water?
Option 1: 15 km/hr
Option 2: 8 km/hr
Option 3: 16 km/hr
Option 4: 12 km/hr
Correct Answer: 12 km/hr
Solution :
Let the speed of the boat = $x$ km/hr
Speed of current = $6$ km/hr
Speed upstream = $(x - 6)$ km/hr
Speed downstream = $(x + 6)$ km/hr
Time of upstream + Time of downstream = 2 hours
$\frac{9}{x-6}+\frac{9}{x+6}= 2$
⇒ $9(x + 6 + x - 6) = 2(x^2 - 36)$
⇒ $9\times2x = 2x^2 - 72$
⇒ $2x^2 - 18x - 72 = 0$
⇒ $x^2 - 9x - 36 = 0$
⇒ $x^2 - 12x + 3x - 36 = 0$
⇒ $x(x - 12) + 3(x - 12) = 0$
⇒ $(x - 12)(x + 3) = 0$
⇒ $x = 12$ (since $x$ can't be negative)
Hence, the correct answer is 12 km/hr.
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