Kelly and Nina are decorating cookies together for the school bake sale. The following equation can be used to find h, the number of hours it will take them to finish decorating the cookies.

Question

h
2
+
h
3
=1
How long will it take Kelly and Nina to decorate the cookies?
Write your answer as a whole number or as a fraction or mixed number in lowest terms.
hours

Answer 1

To solve the equation

\[ \frac{h}{2} + \frac{h}{3} = 1, \]

we first need to find a common denominator for the fractions. The denominators are 2 and 3, and their least common multiple is 6.

Next, we'll rewrite the fractions with a common denominator of 6:

\[ \frac{h}{2} = \frac{3h}{6} \quad \text{and} \quad \frac{h}{3} = \frac{2h}{6}. \]

Substituting these back into the equation gives:

\[ \frac{3h}{6} + \frac{2h}{6} = 1. \]

Now we can combine the fractions on the left side:

\[ \frac{3h + 2h}{6} = 1 \quad \Rightarrow \quad \frac{5h}{6} = 1. \]

To eliminate the fraction, multiply both sides by 6:

\[ 5h = 6. \]

Now, divide both sides by 5 to solve for \( h \):

\[ h = \frac{6}{5}. \]

This can also be expressed as a mixed number:

\[ h = 1 \frac{1}{5}. \]

Thus, the time it will take Kelly and Nina to decorate the cookies is

\[ \boxed{\frac{6}{5}} \text{ hours} \quad \text{or} \quad \boxed{1 \frac{1}{5}} \text{ hours}. \]