Let's solve this problem step-by-step.
1. Determine the individual rates at which Anjali and Eugene pick apples:
- Anjali can pick forty bushels in 14 hours.
- Eugene can pick forty bushels in 11 hours.
Anjali's rate of picking apples:
Anjali picks 40 bushels in 14 hours. Her rate of picking apples is:
[tex]\[
\text{Anjali's rate} = \frac{40 \text{ bushels}}{14 \text{ hours}} \approx 2.857 \text{ bushels per hour}
\][/tex]
Eugene's rate of picking apples:
Eugene picks 40 bushels in 11 hours. His rate of picking apples is:
[tex]\[
\text{Eugene's rate} = \frac{40 \text{ bushels}}{11 \text{ hours}} \approx 3.636 \text{ bushels per hour}
\][/tex]
2. Determine their combined rate of picking apples when they work together:
To find the combined rate, we simply add their individual rates:
[tex]\[
\text{Combined rate} = \text{Anjali's rate} + \text{Eugene's rate} \approx 2.857 + 3.636 \approx 6.494 \text{ bushels per hour}
\][/tex]
3. Determine the time it takes for them to pick forty bushels of apples together:
To find the time taken to pick forty bushels together, we use the total bushels and divide it by their combined rate:
[tex]\[
\text{Time taken together} = \frac{40 \text{ bushels}}{\text{Combined rate}} \approx \frac{40}{6.494} \approx 6.16 \text{ hours}
\][/tex]
Therefore, if Anjali and Eugene work together, it would take them approximately 6.16 hours to pick forty bushels of apples.
