Answer :
Final answer:
Amelia and Keiji can prepare dinner together in approximately 42.35 minutes. Amelia's work rate is 1/90 dinners per minute, while Keiji's is 1/80. Combining their rates gives a total time of 720/17 minutes, or about 42.35 minutes.
Explanation:
Collaborative Dinner Preparation Time
To determine how long it will take Amelia and Keiji to prepare dinner together, we can calculate their individual work rates and then combine them.
Step 1: Calculate Individual Work Rates
- Amelia can prepare dinner for six people in 90 minutes. Therefore, her work rate is 1/90 dinner per minute.
- Keiji can prepare the same dinner in 80 minutes. Thus, his work rate is 1/80 dinner per minute.
Step 2: Combine Their Work Rates
When they work together, their rates add up:
Combined Work Rate = Amelia's rate + Keiji's rate = 1/90 + 1/80
To combine these fractions, we need a common denominator, which is 720:
- For Amelia: 1/90 = 8/720
- For Keiji: 1/80 = 9/720
Now we can add these fractions:
8/720 + 9/720 = 17/720 dinners per minute.
Step 3: Calculate Total Time
The total time T they need to prepare one dinner together can be calculated as follows:
T = 1 / (combined work rate)
T = 1 / (17/720) = 720/17 minutes.
Calculating 720/17 gives approximately 42.35 minutes.
Conclusion
Thus, it will take Amelia and Keiji approximately 42.35 minutes to prepare the dinner if they work together.
Learn more about collaborative work rate here:
https://brainly.com/question/36657461
