Final answer:
To find how long it would take Alberto to pick forty bushels of apples alone, we use the concept of work. We set up an equation using Alberto's rate and time. Solving for time, we find that it would take Alberto approximately 5.23 hours to pick forty bushels of apples alone.
Step-by-step explanation:
To find how long it would take Alberto to pick forty bushels of apples alone, we can use the concept of work. Work is equal to the rate at which a task is completed multiplied by the time taken to complete the task.
Let's let Jack's rate be represented by J, and Alberto's rate be represented by A.
From the given information, we know that Jack can pick forty bushels of apples in 11 hours, so his rate is J = 40 bushels / 11 hours = 40/11 bushels per hour.
When Alberto helps Jack, they together complete the task in 5.24 hours. We can set up the equation A * 5.24 = 40 to represent the work done by Alberto in 5.24 hours. Solving for A, we find that Alberto's rate is A = 40 / 5.24 = 7.63 bushels per hour.
To find how long it would take Alberto to do it alone, we can set up the equation A * t = 40, where t represents the time taken by Alberto alone.
Substituting A = 7.63 bushels per hour, we have 7.63 * t = 40.
Dividing both sides of the equation by 7.63, we find t = 40 / 7.63.
Solving for t, we get t ≈ 5.23 hours.
Therefore, it would take Alberto approximately 5.23 hours to pick forty bushels of apples alone.