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A factory tested three machines that make widgets. The table below shows the data:
\begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Machine \\ A \end{tabular} & \begin{tabular}{c} Machine \\ B \end{tabular} & \begin{tabular}{c} Machine \\ C \end{tabular} \\ \hline Time (hours) & 3 & 6 & 8 \\ \hline Number of widgets & 27 & 42 & 80 \\ \hline \end{tabular}
Write the number of widgets made per hour for each machine.
Number of widgets made per hour by Machine A: [tex]$\square$[/tex]
Number of widgets made per hour by Machine B: [tex]$\square$[/tex]
Number of widgets made per hour by Machine C: [tex]$\square$[/tex]
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]
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