Question: User: Question 3: A machine produces 280 pieces in 3.5 hours. How long does it take to produce 720 pieces? Question 4: Five identical machines produce the same parts at the same rate. The 5 machines complete the required number of parts in 1.8 hours. How many hours does it take 3 machines to produce the same number of parts? Question 5: An annual interest of 551.25 is received on a savings deposit of 10500.00. At the same rate, how much annual interest is received on a deposit of 13090.00?

1. **Problem 1:** A machine produces 280 pieces in 3.5 hours. Find the time to produce 720 pieces. 2. **Formula:** Use the rate formula $$\text{Rate} = \frac{\text{Quantity}}{\text{Time}}$$ and time formula $$\text{Time} = \frac{\text{Quantity}}{\text{Rate}}$$. 3. Calculate the rate of production: $$\text{Rate} = \frac{280}{3.5} = 80 \text{ pieces per hour}$$ 4. Calculate the time to produce 720 pieces: $$\text{Time} = \frac{720}{80} = 9 \text{ hours}$$ --- 5. **Problem 2:** Five identical machines produce parts in 1.8 hours. Find time for 3 machines to produce the same number of parts. 6. Let the total work be the same. The combined rate of 5 machines is: $$\text{Rate}_5 = \frac{\text{Work}}{1.8}$$ 7. Rate of one machine: $$\text{Rate}_1 = \frac{\text{Rate}_5}{5} = \frac{\text{Work}}{5 \times 1.8} = \frac{\text{Work}}{9}$$ 8. Rate of 3 machines: $$\text{Rate}_3 = 3 \times \text{Rate}_1 = 3 \times \frac{\text{Work}}{9} = \frac{\text{Work}}{3}$$ 9. Time for 3 machines: $$\text{Time}_3 = \frac{\text{Work}}{\text{Rate}_3} = \frac{\text{Work}}{\frac{\text{Work}}{3}} = 3 \text{ hours}$$ --- 10. **Problem 3:** Annual interest of 551.25 on 10500.00 deposit. Find interest on 13090.00 at same rate. 11. Calculate interest rate: $$r = \frac{551.25}{10500} = 0.0525$$ 12. Calculate interest on 13090.00: $$I = 13090 \times 0.0525 = 686.72$$ **Final answers:** - Time to produce 720 pieces: 9 hours - Time for 3 machines to produce same parts: 3 hours - Annual interest on 13090.00: 686.72