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?

Pump 1 drains 1/11 pools per minute

Pump 2 drains 1/x pools per minute
(1/11 +1/x)pools/min * 9min = 1 pool
(1/11 + 1/x) =1/9
1/x = 1/9 -1/11 = 11/99 -9/99 = 2/99
so the second pump does 2/99 pool;s per minute or
99/2 minutes per pool

Damon, Im not for sure what the 2/99 stands for.

If the pool has 99 units, then the pump will drain 2 of these units per minute.

To solve this problem, we can use the concept of work rates.

Let's consider the work rate of the first pump to be "x" and the work rate of the second pump to be "y".

We know that the first pump can drain the pool in 11 minutes, so its work rate is 1 pool per 11 minutes, which can be expressed as:
x = 1/11 pool per minute

Similarly, when the second pump is used along with the first pump, they can drain the pool in 9 minutes, so their combined work rate is 1 pool per 9 minutes, which can be expressed as:
(x + y) = 1/9 pool per minute

Now, we need to find the work rate of the second pump when it is the only pump in use. We can assume that the first pump has a work rate of zero when it is not in use. So, the work rate of the second pump would be "y".

Since work rate is inversely proportional to time, we can set up the following equation using the concept of work rate:

(y) = 1/x

Substituting the value of x from the first equation, we have:

(y) = 1/(1/11)
(y) = 11

Therefore, when the second pump is the only pump in use, it would take 11 minutes to drain the pool.