Solution:

1. Determine the combined rate of 3 pumps:

   • If 3 pumps take 7 hours to fill the pool, their combined rate is: $\text{Combined rate of 3 pumps} = \frac{1}{7} \text{ pools per hour.}$ Since this rate is for 3 pumps, the rate of 1 pump is: $\text{Rate of 1 pump} = \frac{1}{7} \div 3 = \frac{1}{21} \text{ pools per hour.}$

2. Determine the combined rate of 2 pumps:

   • Two pumps will have a combined rate of: $\text{Rate of 2 pumps} = 2 \times \frac{1}{21} = \frac{2}{21} \text{ pools per hour.}$

3. Find the time for 2 pumps to fill the pool:

   • The time required is the reciprocal of the combined rate: $\text{Time} = \frac{1}{\frac{2}{21}} = \frac{21}{2} = 10.5 \text{ hours.}$

Final Answer:

Two pumps need 10.5 hours to fill the pool.

Do you want a deeper explanation or have any other questions?
Here are 5 related questions to explore:

1. How would the time change if 4 pumps were used instead of 2 or 3?
2. What is the mathematical formula for determining the time when more or fewer pumps are used?
3. Can you derive the equation for a general number of pumps $n$?
4. What happens if each pump's efficiency decreases over time?
5. How would the solution change if the pumps filled unequal rates?

Tip:

When solving rate problems, always work with rates as "units of work per time" and ensure consistency across all units used!