Math

Please help me, I'm having a hard time setting up this problem.
George can plant a garden in 2 hours, and it takes Joyce 3 hours. They work together for 45 mins, and George leaves and Joyce finishes the job alone. How long does it take Joyce to finish planting the garden?

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  1. job done = rate x time

    George's rate = job/2
    Joyce's rate = job/3
    combined rate = job/2 + job/3 = 5job/6

    let Joyce's time working alone be t hrs

    (3/4) (5job/6) + t(job/3) = job
    divide by job
    (3/4)(5/6) + t/3 = 1
    times 24
    15 + 8t = 24
    8t = 9
    t = 9/8 hrs or (9/8)(60) minutes = 67.5 minutes
    or 1 hour, 7.5 minutes

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    posted by Reiny

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