Pipe A alone takes 9 minutes less than pipe B alone to fill an empty tank. When the tank is empty and both pipes are opened together, it is full in 6 minutes. How long does pipe A alone take to fill the empty tank?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9 minutes
Let A take \(x\) minutes, so B takes \(x+9\) minutes. Their one-minute work added together equals \(\frac{1}{6}\).
\(\displaystyle \frac{1}{x}+\frac{1}{x+9}=\frac{1}{6}\)
\(6(x+9)+6x=x(x+9)\), that is \(12x+54=x^{2}+9x\)
\(x^{2}-3x-54=0\), so \((x-9)(x+6)=0\)
Time cannot be negative, so \(x=9\); then B takes 18 minutes, and \(\displaystyle \frac{1}{9}+\frac{1}{18}=\frac{1}{6}\)
Pipe A alone takes 9 minutes.