algebra

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A can do certain task in 8 hours, B in 10 hours and C in 12 hours. How long will it take to do the task if A and B work 1 hour and then A and C finish the task?

  • algebra -

    rateA&B=1/10+1/8=18/80=9/40
    rateA&c=1/8 +1/12=20/72=10/36

    A. How much of the task is done in the first hour?
    rate*time=9/40*1=9/40
    then how long after the first hour?
    time=amountoftaskLeft/rate=(31/40)/(10/36)= 36*31/40*10=2.79 hours more
    how long= 1+2.79 hours

  • algebra -

    Task = rate x time , let Task = 1

    A's rate = 1/8
    B's rate = 1/10
    C's rate = 1/12
    combined rate of A and B = 1/8+1/10 = 9/40
    combined rate of A and C = 1/8 + 1/12 = 5/24
    let the total time takens to do the job be x hrs
    1(9/40) + (x-1)(5/24) = 1
    multiply each term by 120
    27 + 25(x-1) = 120
    25x - 25 = 93
    25x = 118
    x = 4.72 hrs or 4 hours and appr 43 minutes

  • algebra -

    reiny is correct, my rate for AandC has an error.

  • algebra -

    noted

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