Question

In 5 hours, an experienced cook prepares enough lies to supply a local restaurant’s daily order. Another cook prepares the same number of pies in 6 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 The third cook prepares the pies alone in ? hours

Answer 1

Given:

Number of hours it takes the first cook = 5 hours

Number of hours it takes the second cook = 6 hours

Together with a thrid cook, the number of hours it takes 2 hours.

Let's find the time it will take the third cook to prepare the pie alone.

Let x represent the number of hours it takes the third cook to prepare alone.

Let y represent the number of pies.

We have the following:

• Number of pies the first cook prepares in 1 hour:

$\frac{y}{5}$

• Number of pies the second cook prepares in 1 hour:

$\frac{y}{6}$

• Number of pies the third cook to prepare in one hour:

$\frac{y}{x}$

Number of pies the three cooks prepare altogether in one hour:

$\frac{y}{2}$

Thus, we have the equation:

$\frac{y}{5}+\frac{y}{6}+\frac{y}{x}=\frac{y}{2}$

Let's solve for y in the equation above.

Facor out y from the left side

$y(\frac{1}{5}+\frac{1}{6}+\frac{1}{x})=\frac{y}{2}$

Divide both sides by y:

$\begin{gathered} \frac{y(\frac{1}{5}+\frac{1}{6}+\frac{1}{x})}{y}=\frac{\frac{y}{2}}{y} \\ \\ \frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2} \end{gathered}$

Combine like terms:

$\begin{gathered} \frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2} \\ \\ \frac{6+5}{30}+\frac{1}{x}=\frac{1}{2} \\ \\ \frac{11}{30}+\frac{1}{x}=\frac{1}{2} \end{gathered}$

Subtract 11/30 from both sides:

$\begin{gathered} \frac{11}{30}-\frac{11}{30}+\frac{1}{x}=\frac{1}{2}-\frac{11}{30} \\ \\ \frac{1}{x}=\frac{1}{2}-\frac{11}{30} \\ \\ \frac{1}{x}=\frac{15-11}{30} \\ \\ \frac{1}{x}=\frac{4}{30} \end{gathered}$

Solving further:

$\begin{gathered} \frac{x}{1}=\frac{30}{4} \\ \\ x=7.5 \end{gathered}$

Therefore, the third cook prepares the pies alone in 7.5 hours.

ANSWER:

7.5 hours