Question 78502
You have 1 job ... and that job is cooking the meal.  Since you take 3 hours to do that job,
your rate of doing it is {{{1/3}}} of the job per hour.  Your husband does the 1 job in
2 hours, so his rate of doing the job is {{{1/2}}} of the job per hour.  When you work together
your time to complete the 1 job is represented by t.  The equation becomes:
.
{{{(1/3)*t + (1/2)*t = 1 }}} where the 1 represents the entire job.
.
You can add the terms on the left side either by converting the fractions to decimals or
by putting them over the common denominator of 6.  Let's use the common denominator.
Recognize that {{{1/3 = 2/6}}} and {{{1/2 = 3/6}}}. Substituting these values makes the 
equation become:
.
{{{(2/6)*t + (3/6)*t = 1}}}
.
Now add the two terms on the left side to result in:
.
{{{(2+3)/6*t = 1}}}
.
and this simplifies to:
.
{{{5/6*t = 1}}}
.
you can then solve for t by dividing both sides of this equation by {{{5/6}}} to get:
.
{{{ t = 1/(5/6)}}} and then apply the rule that dividing a quantity by a fraction 
is the same as multiplying the quantity by the inverse of the fraction.  This converts
the equation for t to:
.
{{{t = 1*(6/5) = 6/5}}}
.
and when you divide 5 into 6 you get an answer of 1.2 hours. That's the answer ...
if you and your husband work together you should finish the class in 1.2 hours.
.
Hope this helps you to understand problems of combined efforts a little better.