1. **Problem statement:** It takes 12 hours to fill a swimming pool using 7 identical taps. We want to find how many hours it would take to fill the same size pool using only 4 of these taps. 2. **Formula and concept:** The rate of filling the pool is proportional to the number of taps. If $t$ is the time taken and $n$ is the number of taps, then the work done (filling one pool) is constant. So, $\text{rate} = \frac{1}{t}$ and total work $= \text{rate} \times t = 1$ pool. 3. **Calculate the rate of one tap:** $$\text{Rate of 7 taps} = \frac{1}{12} \text{ pools per hour}$$ Therefore, rate of 1 tap: $$\frac{1}{12} \div 7 = \frac{1}{84} \text{ pools per hour}$$ 4. **Calculate the rate of 4 taps:** $$4 \times \frac{1}{84} = \frac{4}{84} = \frac{1}{21} \text{ pools per hour}$$ 5. **Calculate the time taken by 4 taps:** Since rate $= \frac{1}{\text{time}}$, time $= \frac{1}{\text{rate}}$: $$\text{Time} = \frac{1}{\frac{1}{21}} = 21 \text{ hours}$$ **Final answer:** It will take 21 hours to fill the pool using 4 taps.