Final answer:
If Aliyah and Kathryn worked together, their combined rate would be 11/60 of a field per hour. It would take approximately 5.45 hours for them to harvest the field together.
Step-by-step explanation:
When approaching a problem involving rates of work, it's important to think about the rates at which individuals can complete a task. In this case, we have Aliyah taking 12 hours to harvest a field and Kathryn taking 10 hours. To find how long they would take working together, we should calculate their combined rate of work.
The first step is to determine the rate at which each person can complete the work individually. For Aliyah, this is 1/12 of the field per hour, and for Kathryn, it is 1/10 of the field per hour. To determine their combined rate when working together, we add these rates:
Aliyah's rate: 1/12 field per hour
Kathryn's rate: 1/10 field per hour
Combined rate: 1/12 + 1/10 = 5/60 + 6/60 = 11/60 of the field per hour.
Once the combined rate is found, we can calculate the time it will take both Aliyah and Kathryn to harvest the field together by taking the reciprocal of their combined rate:
Time taken to harvest field together = 1 / (11/60) = 60/11 ≈ 5.45 hours.
Therefore, it would take approximately 5.45 hours for Aliyah and Kathryn to harvest the field if they worked together.