To determine the number of widgets made per hour for each machine, we will use the formula:
[tex]\[
\text{Widgets per hour} = \frac{\text{Number of widgets}}{\text{Time (hours)}}
\][/tex]
Step-by-Step Solution:
1. For Machine A:
[tex]\[
\text{Number of widgets made per hour} = \frac{27}{3} = 9 \text{ widgets per hour}
\][/tex]
Therefore, the number of widgets made per hour by Machine A is [tex]\( 9 \)[/tex].
2. For Machine B:
[tex]\[
\text{Number of widgets made per hour} = \frac{42}{6} = 7 \text{ widgets per hour}
\][/tex]
Therefore, the number of widgets made per hour by Machine B is [tex]\( 7 \)[/tex].
3. For Machine C:
[tex]\[
\text{Number of widgets made per hour} = \frac{80}{8} = 10 \text{ widgets per hour}
\][/tex]
Therefore, the number of widgets made per hour by Machine C is [tex]\( 10 \)[/tex].
Next, we need to determine which machine is the fastest by comparing the number of widgets made per hour by each machine.
- Machine A produces 9 widgets per hour.
- Machine B produces 7 widgets per hour.
- Machine C produces 10 widgets per hour.
Among these, Machine C produces the most widgets per hour.
Thus, the fastest machine is:
[tex]\[
\boxed{\text{Machine C}}
\][/tex]
