Two pipes working together can fill a fish tank in 12 minutes. The first pipe alone fills the tank 10 minutes faster than the second pipe alone. In how many minutes can the second pipe alone fill the tank?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30
Let the faster first pipe take \(x\) minutes; the second takes \(x+10\) minutes. Their one-minute parts add up to \(\frac{1}{12}\).
\(\displaystyle \frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\)
\(12(2x+10)=x(x+10)\)
\(x^{2}-14x-120=0\), that is \((x-20)(x+6)=0\)
Time cannot be negative, so \(x=20\): the first pipe takes 20 minutes
Second pipe \(=20+10=30\) minutes
The second pipe alone fills the tank in 30 minutes.