Rate Problems
Solve the task below:
Dinners and desserts must be made for 180 guests at a reception. There are four chefs responsible for the preparation. The table below shows the preparation rates each of the chefs.
| Chef’s Name | Time needed to make 6 dinners | Time needed to make 6 desserts |
|---|---|---|
| Anna | 12 minutes | 12 minutes |
| Bill | 15 minutes | 9 minutes |
| Carlos | 12 minutes | 10 minutes |
| Dianne | 20 minutes | 6 minutes |
Two chefs will work on dinners while two chefs prepare the desserts.
- Determine which two chefs should work on which preparation to be most efficient.
- Assuming the chefs all start working at the same time, how long will it take to get the meal prepared? If one team finishes before the other, that team can assist the other team in finishing.
Share the solution in two different ways. One of those ways should use at least one rational equation. The other way could use any combination of tables, drawings, pictures, and computation needed. Describe how the two ways of arriving at the answer are related.