Question

The time t required to do a job varies inversely as the number of people working. It takes 7 hr for 6 cooks to prepare the food for a wedding rehearsal dinner. How long will it take 3 cooks toprepare the dinner?It takes 3 cookshr (?) he to prepare the dinner.(Round to the nearest tenth.)

Answer 1

It takes 14 hours for 3 cooks to prepare the dinner.

Explanation:

An inverse variation can be represented by the following equation:

`\begin{gathered} t=(k)/(p) \\ \text{where, } \\ k\text{ is a constant of proportionality} \end{gathered}`

Therefore, if it takes 7 hours for 6 cooks to prepare the food for a wedding, we can substitute this information and find the value of k.

Let t be the time required to do the job.

Let p be the number of people working.

`\begin{gathered} 7=(k)/(6) \\ k=6\cdot7 \\ k=42 \end{gathered}`

Now, knowing the constant, we can substitute it and p=3, into the function to determine how long it takes to prepare the dinner for 3 cooks.

`\begin{gathered} t=(k)/(p) \\ t=(42)/(3) \\ t=14 \end{gathered}`

It takes 14 hours for 3 cooks to prepare the dinner.