Ben's Son

20)  Ben can rake the backyard in 45 minutes.  With his son's
help, they can finish the job in 20 minutes.  How long would it
take Ben's son to rake all the backyard by himself?

Here's a way of looking at this:

        People        Length of Time       Part of Job Done 
        Involved       to Do the Job          in 1 Minute
        --------       -------------       ----------------
          Ben               45                   1/45      
       Ben's son             x                   1/x
        Together            20                   1/20

          1        1         1
         ---  +  -----  =  -----
         45        x         20

Find the Lowest Common Denominator:
               
        45 =          3 * 3 * 5
        20 =  2 * 2 *         5
        -----------------------
              2 * 2 * 3 * 3 * 5 = 180

    L.C.D. = 180x

    180x (1)     180x (1)    180x (1)
        ----  +      ----  =     -----
         45           x            20

    180x / 45 = 4x
    4x * 1 = 4x

    180x / x = 180
    180 * 1 = 180

    180x / 20 = 9x
     9x * 1 = 9x

    4x + 180 = 9x

    180 = 5x

     x = 36 (minutes for the son to rake the entire backyard by
         himself)