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A does 8/15 of a work in 8 days and the remaining work is finished with the assistance of B in 4 days . how long will B take to do the work alone

  • math -

    A's rate = (8/15)W / 8 = W/15
    let B's rate = W/x , where x is the time it would take B to do the job

    combined rate = W/15+W/x = (Wx + 15W)/(15x)

    then 4(Wx + 15W)/(15x) = (7/15)W
    divide by W and expand
    (4x + 60)/(15x) = 7/15
    times 15
    (4x+60)/x = 7
    multiply by x
    4x + 60 = 7x
    x = 20

    it would take B 20 days

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