Let's solve this step-by-step.
1. Determine the production rate per machine in a minute:
We know that 3 machines produce 10 dozen cups in 5 minutes. To find out how many dozen cups one machine produces in one minute, we can break it down:
- In 5 minutes, 3 machines produce 10 dozen cups.
- In 1 minute, these 3 machines will produce [tex]\( \frac{10 \text{ dozen}}{5 \text{ minutes}} = 2 \text{ dozen per minute} \)[/tex].
- So, each machine produces [tex]\( \frac{2 \text{ dozen per minute}}{3 \text{ machines}} = \frac{2}{3} \text{ dozen per machine per minute} \)[/tex].
2. Calculate how many dozen cups 2 machines would produce in one minute:
- If one machine produces [tex]\( \frac{2}{3} \)[/tex] dozen cups in one minute, then 2 machines would produce:
[tex]\[
\frac{2}{3} \text{ dozen per machine per minute} \times 2 \text{ machines} = \frac{4}{3} \text{ dozen per minute}
\][/tex]
3. Determine the total production by 2 machines in one hour (60 minutes):
- If 2 machines produce [tex]\( \frac{4}{3} \)[/tex] dozen cups in one minute, in 60 minutes (which is one hour), they would produce:
[tex]\[
\frac{4}{3} \text{ dozen per minute} \times 60 \text{ minutes} = 80 \text{ dozen}
\][/tex]
Therefore, 2 machines will produce 80 dozen cups in one hour.
