Answer :
A) Using the rate 25 dozen doughnuts per hour, we get:
[tex]6\text{ hours}\cdot\frac{25\text{ dozen}}{1\text{ hour}}=6\cdot25\text{ dozen =}150\text{ dozen of doughnuts}[/tex]B) ) Using the rate 75 dozen doughnuts in 2 hours, we get:
[tex]135\text{ dozen}\cdot\frac{2\text{ hours}}{75\text{ dozen}}=\frac{135\cdot2}{75}hours=3.6\text{ hours}[/tex]C) Let's call x to the number of hours that both machines take to glaze 375 dozen of doughnuts. Similarly than Part A, we need to multiply the number of hours that a machine work by its rate to get the total number of dozen of doughnuts glazed. That is,
[tex]\begin{gathered} \frac{25}{1}x+\frac{75}{2}x=375 \\ \frac{50+75}{2}x=375 \\ \frac{125}{2}x=375 \\ x=375\cdot\frac{2}{125} \\ x=6\text{ hours} \end{gathered}[/tex]D) In 6 hours, the first machine glaze 150 dozen of doughnuts (see part A).
If 375 dozen represents 100%, then we can use the next proportion to find what perentage represents 150 dozen.
[tex]\frac{375\text{ dozen}}{150\text{ dozen}}=\frac{100\text{ \%}}{x\text{ \%}}[/tex]Solving for x,
[tex]\begin{gathered} 375\cdot x=100\cdot150 \\ x=\frac{15000}{375} \\ x=40\text{ \%} \end{gathered}[/tex]