The Three Painters

17)  It would take Jake 60 hours to paint his house.  Dennis could
do it in 50; and Larry, in 53.  If they all work together, how
long will it take?

   1      1        1       1
  --- +  ----  +  ---- =  ----
  60      50       53       x

    Find the least common denominator:

    56 =  2 * 2 * 2 *             7
    60 =  2 * 2 *     3 * 5
    50 =  2 *             5 * 5
    -------------------------------
          2 * 2 * 2 * 3 * 5 * 5 * 7 =  4,200

        L.C.D. = 4,200x

  4,200x (1)     4,200x (1)     4,200x (1)      4,200x (1)
        -----  +        ----  +        ----  =        ------   
         60              50             56              x
                 x

        4,200x / 60 = 70x
        70x * 1 = 70x

        4,200x / 50 = 84x
        84x * 1 = 84x

        4,200x / 56 = 75x
        75x * 1 = 75x

        4,200x / x = 4,200
        4,200 * 1 = 4,200

        70x + 84x +75x = 4,200

        229x = 4,200

        x = 18.34 hours, or 18 hours and 20 minutes