Answer:
Let's assume that the number of pies the two experienced cooks prepare in one hour is x, and the number of pies the third cook prepares in one hour is y.
From the given information, we can write:
The first experienced cook can prepare enough pies for the restaurant's daily order in 5 hours, so their hourly rate of pie preparation is 1/5 of the daily order: x = 1/5
The second experienced cook can prepare the same number of pies in 6 hours, so their hourly rate of pie preparation is x = 1/6
Together with the third cook, they prepare the pies in 2 hours, so their combined hourly rate of pie preparation is 1/2.
Using this information, we can set up the following equation:
1/5 + 1/6 + y = 1/2
To solve for y, we can first find a common denominator:
6/30 + 5/30 + y = 15/30
11/30 + y = 15/30
y = 4/30
So the third cook can prepare 4/30 of the daily order in one hour. To find out how long it would take them to prepare the entire daily order alone, we can set up the equation:
4/30t = 1
where t is the time it takes the third cook to prepare the daily order alone.
Solving for t, we get:
t = 30/4 = 7.5 hours
Therefore, it takes the third cook 7.5 hours to prepare the pies for the restaurant's daily order alone.