Bobby takes 15 mins to prepare 3 1/4 cups of juice.
Lets find out how long does he takes to prepare 1 cup of juice.
[tex]3 \dfrac{1}{4} \text { cups = } 15 \text { mins}[/tex]
Divide by 3 1/4 on both sides:
[tex]\text { 1 cups = } 15 \div 3 \dfrac{1}{4} \text { mins}[/tex]
Change to improper fraction:
[tex]\text { 1 cups = } 15 \div \dfrac{13}{4} \text { mins}[/tex]
Change the divide fraction to multiplication fraction:
[tex]\text { 1 cups = } 15 \times \dfrac{4}{13} \text { mins}[/tex]
Combine into single fraction:
[tex]\text { 1 cups = } \dfrac{60}{13} \text { mins}[/tex]
Find time needed to prepare 32 1/2 cups of juice
[tex]\text { 1 cups = } \dfrac{60}{13} \text { mins}[/tex]
[tex]32 \dfrac{1}{2} \text { cups = } \dfrac{60}{13} \times 32 \dfrac{1}{2} \text { mins}
[/tex]
[tex]32 \dfrac{1}{2} \text { cups = } \dfrac{60}{13} \times \dfrac{65}{2} \text { mins}[/tex]
[tex]32 \dfrac{1}{2} \text { cups = } 150 \text { mins}[/tex]
Convert mins to hours
[tex]\text {Number of hours = } 150 \div 60 [/tex]
[tex]\text {Number of hours = } 2 \dfrac{1}{2} [/tex]
[tex]\bf \text {Answer: Bobby needs } 2 \dfrac{1}{2} \text { hours to make } 32 \dfrac{1}{2} \text { cups of juice. }[/tex]