1. Problem: A contractor hires 8 workers. How many workers are available? This is a straightforward statement, so the answer is simply 8 workers. 2. Problem: A water tank can be filled by 6 taps in 15 minutes. How long will it take to fill the tank if only 4 taps are used? Formula: Time \( T \) is inversely proportional to the number of taps \( n \), so \( T \times n = \text{constant} \). Calculation: $$6 \times 15 = 4 \times T$$ $$T = \frac{6 \times 15}{4} = 22.5 \text{ minutes}$$ 3. Problem: 5 machines manufacture 100 units in 2 hours. How many units are manufactured in 2 hours if 10 machines are used? Formula: Units produced \( U \) is directly proportional to the number of machines \( m \). Calculation: $$\frac{100}{5} = \frac{U}{10} \Rightarrow U = \frac{100}{5} \times 10 = 200 \text{ units}$$ 4. Problem: Some machines produce 80 widgets in 6 minutes. How many minutes will it take to produce the same number of widgets if the production rate is doubled? Formula: Time \( T \) is inversely proportional to the production rate \( R \). Calculation: $$T = \frac{6}{2} = 3 \text{ minutes}$$ 5. Problem: A bakery produces 200 loaves in 5 hours. How many hours to produce 350 loaves? Formula: Time \( T \) is directly proportional to the number of loaves \( L \). Calculation: $$\frac{200}{5} = \frac{350}{T} \Rightarrow T = \frac{350 \times 5}{200} = 8.75 \text{ hours}$$ 6. Problem: A printer prints 500 copies in 4 hours. How long to print 350 copies? Formula: Time \( T \) is directly proportional to the number of copies \( C \). Calculation: $$\frac{500}{4} = \frac{350}{T} \Rightarrow T = \frac{350 \times 4}{500} = 2.8 \text{ hours}$$ 7. Problem: 15 workers paint a house in 6 days. If the deadline is 4 days, how many additional workers are needed? Formula: Number of workers \( W \) is inversely proportional to time \( T \) for the same work. Calculation: $$15 \times 6 = W \times 4 \Rightarrow W = \frac{15 \times 6}{4} = 22.5 \approx 23 \text{ workers}$$ Additional workers needed: $$23 - 15 = 8$$ 8. Problem: A tank can be filled by a pump in 20 minutes. How long will it take to fill the tank if... (incomplete question, cannot solve). Final answers: 1) 8 workers 2) 22.5 minutes 3) 200 units 4) 3 minutes 5) 8.75 hours 6) 2.8 hours 7) 8 additional workers 8) Insufficient data