Working alone, it takes Anjali 14 hours to
pick forty bushels of apples. Eugene can
pick the same amount in 11 hours. If they
worked together how long would it take
them?



Answer :

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.