Question

working together, two pumps can drain a certain pool in 4 hours. if it takes the older pump 9 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own? do not do any rounding.

Explanation:

Step1: Define rates

Let $t$ = time (hours) for newer pump alone.
Older pump rate: $\frac{1}{9}$ pool/hour.
Newer pump rate: $\frac{1}{t}$ pool/hour.
Combined rate: $\frac{1}{4}$ pool/hour.

Step2: Set up combined rate equation

$$\frac{1}{9} + \frac{1}{t} = \frac{1}{4}$$

Step3: Solve for $\frac{1}{t}$

$$\frac{1}{t} = \frac{1}{4} - \frac{1}{9}$$
$$\frac{1}{t} = \frac{9 - 4}{36} = \frac{5}{36}$$

Step4: Find $t$

$$t = \frac{36}{5}$$

Answer:

$\frac{36}{5}$ hours