Question

At the ice cream factory you manage you have a rush order for 1200 gallons of wainut fudge ice cream. One machine can produce 100 gallons of ice cream every 80 minutes. If you start production on that machine at 6:00 am, about what time will be production run end end?

Answer 1

Given that the machine takes 80 minutes to produce 100 gallons of ice cream, so the rate of production (r) is given by,

`\begin{gathered} r=(100)/(80) \\ r=1.25\text{ gallons/min} \end{gathered}`

So the time required to produce 1200 gallons of the ice cream is calculated as,

`\begin{gathered} t=(1200)/(r) \\ t=(1200)/(1.25) \\ t=960\text{ min} \end{gathered}`

Thus, 960 minutes are required for producing 1200 gallons of ice cream.

Converting into hours,

`\begin{gathered} 960\text{ minutes=}(960)/(60)\text{ hours} \\ 960\text{ minutes=}16\text{ hours} \end{gathered}`

The time 16 hours after 6:00 am will be 22:00 which corresponds to 10:00 pm.

Therefore, the product run will end at 10:00 pm.