Mathematics, 13.02.2020 20:14 graciewilson

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.

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Answer from: lovedavis9544

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

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

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

Not sure what the question is but i hope this x = years100 * x

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