1. **State the problem:** We have a machine that fills a form of dimensions 50 cm wide, 1 m high, and 1.5 m long in 15 minutes. We want to find how long 10 machines take to fill a larger form of dimensions 10 m wide, 10 m long, and 3 m high. 2. **Convert all dimensions to meters:** - Original form width: 50 cm = 0.5 m - Original form height: 1 m - Original form length: 1.5 m 3. **Calculate the volume of the original form:** $$V_1 = 0.5 \times 1 \times 1.5 = 0.75 \text{ cubic meters}$$ 4. **Calculate the volume of the larger form:** $$V_2 = 10 \times 3 \times 10 = 300 \text{ cubic meters}$$ 5. **Calculate the time taken by one machine to fill the larger form:** Since time is proportional to volume for one machine, $$t_1 = 15 \text{ minutes}$$ $$t_2 = t_1 \times \frac{V_2}{V_1} = 15 \times \frac{300}{0.75} = 15 \times 400 = 6000 \text{ minutes}$$ 6. **Calculate the time taken by 10 machines working together:** Time is inversely proportional to the number of machines, $$t_{10} = \frac{t_2}{10} = \frac{6000}{10} = 600 \text{ minutes}$$ 7. **Convert minutes to hours:** $$600 \text{ minutes} = \frac{600}{60} = 10 \text{ hours}$$ **Final answer:** It takes 10 machines 10.0 hours to fill the larger form.