Answer:
![9\frac{1}{3}hours](https://tex.z-dn.net/?f=9%5Cfrac%7B1%7D%7B3%7Dhours)
Step-by-step explanation:
Let third cook take x hours to prepare the same number of pies y alone
Let y be the number of pies
In 1 hour ,third cook prepare pies=![\frac{y}{x}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Bx%7D)
One experienced cook takes time to prepare enough pies =4 hours
In 1 hour , cook prepare pies=![\frac{y}{4}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B4%7D)
Another cook takes time to prepare same number of pies =7 hours
In 1 hour , another cook prepare pies=![\frac{y}{7}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B7%7D)
All three cooks take time to prepare the same number of pies=2 hours
In 1 hour,all three cooks prepare pies=![\frac{y}{2}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B2%7D)
According to question
![\frac{y}{4}+\frac{y}{7}+\frac{y}{x}=\frac{y}{2}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B4%7D%2B%5Cfrac%7By%7D%7B7%7D%2B%5Cfrac%7By%7D%7Bx%7D%3D%5Cfrac%7By%7D%7B2%7D)
![y(\frac{1}{4}+\frac{1}{7}+\frac{1}{x})=\frac{y}{2}](https://tex.z-dn.net/?f=y%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B7%7D%2B%5Cfrac%7B1%7D%7Bx%7D%29%3D%5Cfrac%7By%7D%7B2%7D)
![\frac{1}{4}+\frac{1}{7}+\frac{1}{x}=\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B7%7D%2B%5Cfrac%7B1%7D%7Bx%7D%3D%5Cfrac%7B1%7D%7B2%7D)
![\frac{1}{x}=\frac{1}{2}-\frac{1}{4}-\frac{1}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%3D%5Cfrac%7B1%7D%7B2%7D-%5Cfrac%7B1%7D%7B4%7D-%5Cfrac%7B1%7D%7B7%7D)
![\frac{1}{x}=\frac{14-7-4}{28}=\frac{3}{28}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%3D%5Cfrac%7B14-7-4%7D%7B28%7D%3D%5Cfrac%7B3%7D%7B28%7D)
hours
Hence, the third cook takes time to prepare the same number of pies alone=![9\frac{1}{3}hours](https://tex.z-dn.net/?f=9%5Cfrac%7B1%7D%7B3%7Dhours)