Hi I’m having trouble with a math question. If someone could help me out on how to do the whole problem it would be greatly appreciated. The math problem is below:

One pump can drain a pool in 5 minutes. When a second pump is also used, the pool only takes 4 minutes to drain the pool. How long would it take the second pump to drain the pool if it were the only pump in use?

T1*T2/(T1+T2) = 4.

5*T2/(5+T2) = 4,
5T2 = 20+4T2,
T2 = __Min. = Time for 2nd pump to drain pool.

in 4 minutes, the 1st pump drains 80% of the pool ... 4 / 5 = 80%

this means that in 4 minutes, the 2nd pump drained 1/5 of the pool
... draining the whole thing would take 5 times as long ... 4 * 5 = 20

To solve this problem, let's break it down step by step.

Step 1: Let's assume the volume of the pool is "V" (this value is not necessary for solving the problem)
Step 2: Since one pump can drain the pool in 5 minutes, the rate at which this pump drains the pool is 1/5 of the pool per minute. Therefore, the first pump's rate of draining the pool is 1/5V per minute.
Step 3: When the second pump is used in addition to the first pump, the combined rate of both pumps is such that the pool is drained in 4 minutes. This means the combined rate of draining the pool is 1/4 of the pool per minute.
Step 4: Now, let's denote the rate at which the second pump drains the pool by "x" (in units of 1 pool per minute). Since the combined rate of both pumps is 1/4, the equation would be:
1/5 + x = 1/4

Step 5: To solve for "x", we need to isolate it on one side of the equation. We can do this by subtracting 1/5 from both sides:
x = 1/4 - 1/5

Now, let's simplify this expression:

Step 6: To subtract fractions, we need to find a common denominator. In this case, the common denominator between 4 and 5 is 20. Rewriting the expression with the common denominator gives us:
x = 5/20 - 4/20

Step 7: Now we can subtract the numerators:
x = 1/20

Step 8: So, we found that the rate at which the second pump drains the pool is 1/20 of the pool per minute.

Step 9: Finally, to find out how long it would take the second pump, on its own, to drain the pool completely, we need to calculate the reciprocal of its rate. So the reciprocal of 1/20 is 20/1.

Step 10: Therefore, on its own, the second pump would take 20 minutes to drain the pool.

To summarize, if the first pump takes 5 minutes to drain the pool and when the second pump is used in addition to the first, the pool drains in 4 minutes, then the second pump would take 20 minutes to drain the pool on its own.