Question 78502
<pre><font size = 4><b>
It takes me 3 hours to prepare a special dinner in class,
when it only took my husband 2 hours. How long will it 
take for them both to finish the cooking class? Answer 
should be rounded to the one decimal. Must be shown in a 
rational equation.

Let the answer be x hours.

The secret in doing this kind of problem is

1. Take everything down to 1 hour, 
2. Then take everything up to x hours.

>>...It takes me 3 hours to prepare a special dinner...<<

1. So therefore in 1 hour I can prepare 1/3 of a special dinner.
2. So therefore in x hours I can prepare x/3 of a special dinner.

>>...it...took my husband 2 hours...<<

1. So therefore in 1 hour my husband can prepare 1/2 of a special dinner.
2. So therefore in x hours my husband can prepare x/2 of a special dinner.

So therefore the equation comes from:

   The part of a dinner I can do in x hours +
         The part of a dinner my husband can do in x hours =
                1 dinner.

So the equation is

                    {{{x/3 + x/2 = 1}}}

Multiply through by LCD = 6

                    {{{(6x)/3 + (6x)/2 = 6}}}

                    {{{2x + 3x = 6}}}

                    {{{5x = 6}}}

Divide both sides by 5

                    {{{(5x)/5 = 6/5}}}

                    {{{x = 1.2}}}

Answer: 1.2 hours (or 1 hour and 12 minutes.)

Edwin</pre>