Question

factory a can produce 55 machines in 25 minutes. factory b can produce 35 machines in 20 minutes. if both factories produce machines for 3 hours, which factory will produce more machines? how many more machines will be produced? factory a can produce \boxed{} machines in three hours. factory b can produce \boxed{} machines in three hours. factory \boxed{} produces more machines in three hours. this factory produces \boxed{} more machines than the other factory in three hours.

Explanation:

Step1: Convert 3 hours to minutes

3 hours = 3 * 60 = 180 minutes.

Step2: Calculate production rate of Factory A

Factory A produces 55 machines in 25 minutes. So rate \( r_A = \frac{55}{25} \) machines per minute. In 180 minutes, production \( P_A = \frac{55}{25} \times 180 \). Simplify: \( \frac{55 \times 180}{25} = 55 \times 7.2 = 396 \) machines.

Step3: Calculate production rate of Factory B

Factory B produces 35 machines in 20 minutes. Rate \( r_B = \frac{35}{20} \) machines per minute. In 180 minutes, production \( P_B = \frac{35}{20} \times 180 \). Simplify: \( \frac{35 \times 180}{20} = 35 \times 9 = 315 \) machines.

Step4: Compare productions and find difference

\( P_A = 396 \), \( P_B = 315 \). Difference \( 396 - 315 = 81 \).

Answer:

Factory A can produce \(\boldsymbol{396}\) machines in three hours.
Factory B can produce \(\boldsymbol{315}\) machines in three hours.
Factory \(\boldsymbol{A}\) produces more machines in three hours. This factory produces \(\boldsymbol{81}\) more machines than the other factory in three hours.