In 4 ​hours, an experienced cook prepares enough pies to supply a local​ restaurant’s daily order. Another cook prepares the same number of

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.

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Hailey 4 weeks 2021-12-30T22:36:39+00:00 1 Answer 0 views 0

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    2021-12-30T22:38:11+00:00

    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

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45:7+7-4:2-5:5*4+35:2 =? ( )