Question

In 4 ​hours, an experienced cook prepares enough pies to supply a local​ restaurant's daily order. Another cook prepares the same number of pies in 7 hours. Together with a third​ cook, they prepare the pies in 2 hours. Find how long it takes the third cook to prepare the pies alone.

Answer 1

`9(1)/(3)hours`

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=
`(y)/(x)`

One experienced cook takes time to prepare enough pies =4 hours

In 1 hour , cook prepare pies=
`(y)/(4)`

Another cook takes time to prepare same number of pies =7 hours

In 1 hour , another cook prepare pies=
`(y)/(7)`

All three cooks take time to prepare the same number of pies=2 hours

In 1 hour,all three cooks prepare pies=
`(y)/(2)`

According to question

`(y)/(4)+(y)/(7)+(y)/(x)=(y)/(2)`

`y((1)/(4)+(1)/(7)+(1)/(x))=(y)/(2)`

`(1)/(4)+(1)/(7)+(1)/(x)=(1)/(2)`

`(1)/(x)=(1)/(2)-(1)/(4)-(1)/(7)`

`(1)/(x)=(14-7-4)/(28)=(3)/(28)`

`x=(28)/(3)=9(1)/(3)` hours

Hence, the third cook takes time to prepare the same number of pies alone=
`9(1)/(3)hours`