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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.

Respuesta :

lublana

Answer:

[tex]9\frac{1}{3}hours[/tex]

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=[tex]\frac{y}{x}[/tex]

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

In 1 hour , cook prepare pies=[tex]\frac{y}{4}[/tex]

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

In 1 hour , another cook prepare pies=[tex]\frac{y}{7}[/tex]

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

In 1 hour,all three cooks  prepare  pies=[tex]\frac{y}{2}[/tex]

According to question

[tex]\frac{y}{4}+\frac{y}{7}+\frac{y}{x}=\frac{y}{2}[/tex]

[tex]y(\frac{1}{4}+\frac{1}{7}+\frac{1}{x})=\frac{y}{2}[/tex]

[tex]\frac{1}{4}+\frac{1}{7}+\frac{1}{x}=\frac{1}{2}[/tex]

[tex]\frac{1}{x}=\frac{1}{2}-\frac{1}{4}-\frac{1}{7}[/tex]

[tex]\frac{1}{x}=\frac{14-7-4}{28}=\frac{3}{28}[/tex]

[tex]x=\frac{28}{3}=9\frac{1}{3}[/tex] hours

Hence, the third cook takes time to prepare the same number of pies alone=[tex]9\frac{1}{3}hours[/tex]