SOLUTION: 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 ro

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Question 78502: 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
Found 2 solutions by Edwin McCravy, bucky:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

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%2F3+%2B+x%2F2+=+1

Multiply through by LCD = 6

                    %286x%29%2F3+%2B+%286x%29%2F2+=+6

                    2x+%2B+3x+=+6

                    5x+=+6

Divide both sides by 5

                    %285x%29%2F5+=+6%2F5

                    x+=+1.2

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

Edwin

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F3 of the job per hour. Your husband does the 1 job in
2 hours, so his rate of doing the job is 1%2F2 of the job per hour. When you work together
your time to complete the 1 job is represented by t. The equation becomes:
.
%281%2F3%29%2At+%2B+%281%2F2%29%2At+=+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%2F3+=+2%2F6 and 1%2F2+=+3%2F6. Substituting these values makes the
equation become:
.
%282%2F6%29%2At+%2B+%283%2F6%29%2At+=+1
.
Now add the two terms on the left side to result in:
.
%282%2B3%29%2F6%2At+=+1
.
and this simplifies to:
.
5%2F6%2At+=+1
.
you can then solve for t by dividing both sides of this equation by 5%2F6 to get:
.
+t+=+1%2F%285%2F6%29 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%2A%286%2F5%29+=+6%2F5
.
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.