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In the MasterChef kitchen, contestants Tom and Sarah are working together on a five-course meal for the judges. Tom is responsible for cooking the main components of each dish, while Sarah handles all the sauces and garnishes. They must complete all courses, but the order doesn’t matter. However, Tom must finish cooking a dish before Sarah can start on its sauce and garnish. Both Tom and Sarah can only work on one dish at a time.
The cooking and garnishing times for each course are shown in the table.
If Tom and Sarah start working at 5:00 p.m., what is the earliest time they can have all five courses ready for the judges? Justify your answer.
Let’s approach this step-by-step:
1. First, we calculate the total cooking time and total sauce/garnish time:
– Total cooking time: 15 + 60 + 40 + 35 + 25 = 175 minutes
– Total sauce/garnish time: 25 + 20 + 10 + 30 + 15 = 100 minutes
2. Since 175 > 100, the cooking will take longer than the sauce/garnish preparation. The minimum time required will be at least 175 minutes, plus the time for Sarah to finish the sauce/garnish for the last dish Tom cooks.
3. To minimize the overall time, we should:
a) Have Tom start with dishes that have shorter cooking times, so Sarah can start working sooner.
b) End with dishes that have shorter sauce/garnish times, so Sarah finishes as soon as possible after Tom.
4. Let’s order the dishes based on these criteria
| Course | Cooking Time | Sauce/Garnish Time |
|---|---|---|
| 1 | 15 | 25 |
| 5 | 25 | 15 |
| 4 | 35 | 30 |
| 3 | 40 | 10 |
| 2 | 60 | 20 |
5. The optimal order would be: 1, 5, 4, 3, 2
6. Now let’s create a timeline:
Tom: [1:15][5:25 ][4:35 ][3:40 ][2:60 ]
Sarah: [1:25 ][5:15][4:30 ][3:10][2:20 ]
7. The total time is 175 minutes for Tom’s cooking, plus 20 minutes for Sarah to finish the last dish, totaling 195 minutes.
8. 195 minutes = 3 hours and 15 minutes
Therefore, if Tom and Sarah start at 5:00 p.m., they will finish at 8:15 p.m. at the earliest.
This solution ensures that Sarah is working as much as possible while Tom is cooking, and minimizes the time Sarah needs after Tom finishes his last dish.