One pump can drain the pool in 11 minutes. When a second pump is used, it only takes 9 minutes. How long would it take the second pump to drain the pool if it were the only pump in use?
To find out how long it would take the second pump to drain the pool if it were the only pump in use, we can use the concept of "work rates." The work rate of a pump is the amount of work it can do in a given unit of time.
Let's denote the work rate of the first pump as R1 (measured in pool volumes per minute) and the work rate of the second pump as R2 (also measured in pool volumes per minute).
We are given the following information:
1) The first pump takes 11 minutes to drain the pool.
2) When the second pump is used along with the first pump, the pool is drained in 9 minutes.
Using this information, we can set up the following equation:
1/R1 + 1/R2 = 1/T
where T represents the time it would take for the second pump to drain the pool if it were the only pump in use.
Let's plug in the known values into the equation:
1/11 + 1/9 = 1/T
To solve for T, we can simplify this equation. First, we will find a common denominator:
(9 + 11)/99 = 1/T
20/99 = 1/T
To isolate T, we can take the reciprocal of both sides:
99/20 = T
Therefore, the second pump would take 99/20 minutes to drain the pool if it were the only pump in use. Simplifying this, we find it would take approximately 4.95 minutes.