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

Answer:

$9\frac{1}{3}hours$

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=$\frac{y}{x}$

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

In 1 hour , cook prepare pies=$\frac{y}{4}$

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

In 1 hour , another cook prepare pies=$\frac{y}{7}$

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

In 1 hour,all three cooks  prepare  pies=$\frac{y}{2}$

According to question

$\frac{y}{4}+\frac{y}{7}+\frac{y}{x}=\frac{y}{2}$

$y(\frac{1}{4}+\frac{1}{7}+\frac{1}{x})=\frac{y}{2}$

$\frac{1}{4}+\frac{1}{7}+\frac{1}{x}=\frac{1}{2}$

$\frac{1}{x}=\frac{1}{2}-\frac{1}{4}-\frac{1}{7}$

$\frac{1}{x}=\frac{14-7-4}{28}=\frac{3}{28}$

$x=\frac{28}{3}=9\frac{1}{3}$ hours

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