FACTORIES A factory produces 6 motorcycles in 9 hours. Write proportion and solve it to find many hours it takes to produce 16 motorcycles.

To set up the proportion, we know that 6 motorcycles take 9 hours. We can express this as a fraction: \( \frac{6 \text{ motorcycles}}{9 \text{ hours}} \). Now we want to find out how many hours (let's call it \( x \)) it takes to produce 16 motorcycles, so we set up the equation: \( \frac{6}{9} = \frac{16}{x} \). Now, cross-multiply: \( 6x = 16 \times 9 \). Simplifying, we find \( 6x = 144 \). Now, divide both sides by 6 to isolate \( x \): \( x = 24 \). Thus, it takes 24 hours to produce 16 motorcycles. To further validate our finding, you can check the production rate. Each motorcycle takes 1.5 hours (9 hours ÷ 6 motorcycles). So, for 16 motorcycles, multiplying 16 by 1.5 gives you 24 hours. This consistency is a great way to ensure your calculations are correct!