Respuesta :
Answer:
It takes 14 hours for 3 cooks to prepare the dinner.
Step-by-step explanation:
An inverse variation can be represented by the following equation:
[tex]\begin{gathered} t=\frac{k}{p} \\ \text{where, } \\ k\text{ is a constant of proportionality} \end{gathered}[/tex]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.
[tex]\begin{gathered} 7=\frac{k}{6} \\ k=6\cdot7 \\ k=42 \end{gathered}[/tex]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.
[tex]\begin{gathered} t=\frac{k}{p} \\ t=\frac{42}{3} \\ t=14 \end{gathered}[/tex]It takes 14 hours for 3 cooks to prepare the dinner.
