The Bookcase

    19)  In his shop, Chuck can make a good bookcase in 5 hours.
After working on one for 2 hours, however, he let his son finish
it.  The son has made bookcases before, but it takes him 8 hours
to make one.  How many hours will it take for the son to complete
his father's bookcase?  

    For this problem, we will first figure how much of the project
is left for the son to do.  Since his father can build a bookcase
in 5 hours and already worked two hours on it, then 2/5 of the
project is complete; and, therefore, 3/5 more for the son to do.

        So here's our formula:

           1       1       3
         ----- = ----- * -----
           8       x       5

    In the first fraction, we have  the time it takes the son
to do a complete project: 1/8  per hour.  The second fraction
contains the variable we are seeking the value of -- how many
hours it will take the son.  And the 3/5 is how much of the project
he has to work on.

    Multiply the two fractions to the right of the equal side:

           1       3
         ----- = -----
           8       5x

    Find the least common denominator:

    L.C.D. = 40x

       40x (1)    40x (3)
          ----  =    -----
            8          5x
               
    40x / 8 = 5x
    5x * 1 = 5x

    40x /5x = 8 (x's cancel out)
    8 * 3 = 24

    5x = 24

    x = 4.8 hours or 4 hours and 48 minutes.