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Math Help - I need HELP FAST!!!

  1. #1
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    I need HELP FAST!!!

    it takes Bill 2 hours longer to do a job than jerry. they work together for 2 hours; then jerry takes over and completed the job in 1 hour. how long would it take arch along to do the job?
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Brooke
    it takes Bill 2 hours longer to do a job than jerry. they work together for 2 hours; then jerry takes over and completed the job in 1 hour. how long would it take arch along to do the job?
    Let jerry completes the work in x hours, and bill in (x+2)hours
    now, jerry works for 3 hous and bill for two hours to complete the job
    hence,
    \frac{3}{x}+\frac{2}{x+2}=1
    3x+6+2x=x^2+2x
    x^2-3x-6=0
    Value of x,x+2 gives your answer.

    KeepSmiling
    Malay
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  3. #3
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    Hello, Brooke!

    It takes Bill 2 hours longer to do a job than Jerry.
    They worked together for 2 hours, then Jerry took over and completed the job in 1 hour.
    How long would it take each alone to do the job?

    Malay gave you an excellent explanation.
    Let me give you my baby-talk version . . .


    It takes Jerry x hours to do the job alone.
    . . In one hour, he can do \frac{1}{x} of the the job.
    He worked 3 hours, so he completed \frac{3}{x} of the job.


    It takes Bill x + 2 hours to do the job alone.
    . . In one hour, he can do \frac{1}{x+2} of the job.
    He worked 2 hours, so he completed \frac{2}{x+2} of the job.


    Together, they competed the job ("1 whole job").
    . . And there is our equation: . \frac{3}{x} + \frac{2}{x+2}\:=\:1


    Multiply through by the LCD: x(x+2):
    . . x(x+2)\cdot\frac{3}{x} \:+ \:x(x+2)\cdot\frac{2}{x+2}\;\;=\;\;x(x+2)\cdot1

    We have: . 3(x +2) + 2x \;= \;x(x + 2)

    . . which simplifies to the quadratic: . x^2 - 3x - 6 \;= \;0

    . . Quadratic Formula: . x\;=\;\frac{-(-3) \pm\sqrt{(-3)^2 - 4(1)(-6)}}{2(1)}

    . . and has the positive root: . x \:= \:\frac{3 + \sqrt{33}}{2}


    Therefore: Jerry takes \frac{3 + \sqrt{33}}{2}\:\approx\;4.37 hours to do the job alone

    . . . . and: Bill takes \frac{7 + \sqrt{33}}{2}\:\approx\:6.37 hours to do the job alone.


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