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Math Help - Intermediate Algebra Problems

  1. #1
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    Intermediate Algebra Problems

    Can someone pleace explain how to solve these problems?
    The problem statement, all variables and given/known data
    Sally can paint a room in 9 hours while it takes Steve 3 hours to paint the same room. How long would it take them to paint the room if they worked together?
    The problem statement, all variables and given/known data
    One hose can fill a goldfish pond in 18 minutes, and two hoses can fill the same pond in 14 minutes. Find how long it takes the second hose alone to fill the pond.
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  2. #2
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    Re: Intermediate Algebra Problems

    1. Set these up as ratios "How much of the room painted : Hours".

    Sally
    \displaystyle 1 : 9 = \frac{1}{9} : 1


    Steve
    \displaystyle 1 : 3 = \frac{1}{3} : 1


    Together
    \displaystyle \begin{align*} \frac{1}{9} + \frac{1}{3} &: 1 \\ \frac{4}{9} &: 1 \\ 4 &: 9 \\ 1 &: \frac{9}{4} \end{align*}.

    So together they will take \displaystyle 2\frac{1}{4} hours.
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  3. #3
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    Re: Intermediate Algebra Problems

    For the second one, lets call the hoses hose A and hose B. A takes 18 minutes so the ratio is 18:1. A+B would be 14:1, so 1/14-1/18=1/63. Hence it is 63 minutes...
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  4. #4
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    Re: Intermediate Algebra Problems

    A slightly different point of view: when people or things "work together", their rates of work add.

    "Sally can paint a room in 9 hours"
    so Sally's rate of work is 1/9 "room per hour".
    "it takes Steve 3 hours to paint the same room"
    so Steve's rate of work is 1/3 "room per hour".

    Together they work at \frac{1}{9}+ \frac{1}{3}= \frac{1}{9}+ \frac{3}{9}= \frac{4}{9} "room per hour". Invert that to get "hours per room".

    "One hose can fill a goldfish pond in 18 minutes"
    so that hose works at 1/18 "pond per minute". Since we want to find how long it would take the second hose to fill the pond, call that time "x" minutes. The
    second hose works at 1/x "pond per minute".
    " and two hoses can fill the same pond in 14 minutes."
    so \frac{1}{18}+ \frac{1}{x}= \frac{1}{14}

    Solve that for x. I recommend multiplying both sides of the equation by the "least common denominator", 2(7)(9)x= 126x.
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  5. #5
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    Re: Intermediate Algebra Problems

    thanks everybody for the explanations! i understand it now!
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