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Math Help - [SOLVED] Twist on Work Rate Problem

  1. #1
    Paul B
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    [SOLVED] Twist on Work Rate Problem

    I am trying to show my students a different slant on a work rate problem and I want to make sure I show them the best method.

    Working together, Nina and Lauren can mow the lawn in 2 hours. It takes Nina 3/4 as long as Lauren to do the job alone. How long would it take Nina working alone?

    I appreciate the help. My applied Algebra kids struggle with these.

    Paul
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  2. #2
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    Quote Originally Posted by Paul B View Post
    I am trying to show my students a different slant on a work rate problem and I want to make sure I show them the best method.

    Working together, Nina and Lauren can mow the lawn in 2 hours. It takes Nina 3/4 as long as Lauren to do the job alone. How long would it take Nina working alone?

    I appreciate the help. My applied Algebra kids struggle with these.

    Paul
    I use a formula I developed.

    If "a" and "b" are the times one person completes a job and another completes a hour (say in hours).

    Then working together it takes,
    (ab)/(a+b)
    Hours.

    Thus,
    (NL)/(N+L)=2

    And

    N=L+3/4

    Now use this system.
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  3. #3
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    Hello, Paul!

    I'll do it the old-fashioned way . . .


    Working together, Nina and Lauren can mow the lawn in 2 hours.
    It takes Nina as long as Lauren to do the job alone.
    How long would it take Nina working alone?

    Let N = number of hours for Nina to mow the lawn alone.
    Let L = number of hours for Lauren to mow the lawn alone.

    In one hour, Nina can mow 1/N of the lawn.
    In one hour, Lauren can mow 1/L of the lawn.

    Together, it takes them 2 hours to mow the lawn.
    So in one hour, they can mow of the lawn.

    We have: .1/N + 1/L .= .1/2 . . 2L + 2N .= .LN . [1]


    We are told that: .N = L

    Substitute into [1]: .2L + 2(L) .= .L(L)

    Multiply by 4/L: .8 + 6 .= .3L . . L = 14/3

    Then: .N .= .(3/4)(14/3) .= .7/2


    Therefore, working alone, Nine will take 3 hours.

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