Esther the Clown does face painting at the city carnival. She paints 7 faces every 21 minutes and spends the same amount of time painting each face. Write an equation that relates $$ f $$, the number of faces she paints, and $$ m $$, the time she spends painting in minutes.

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To relate $$ f $$ (the number of faces Esther paints) and $$ m $$ (the time she spends painting in minutes), we can use the given rate:

- Esther paints **7 faces** in **21 minutes**.

First, determine the time it takes to paint **one face**:
$$
\text{Time per face} = \frac{21 \text{ minutes}}{7 \text{ faces}} = 3 \text{ minutes per face}
$$

Now, to find the number of faces painted ($$ f $$) based on the total time spent ($$ m $$):
$$
f = \frac{m}{3}
$$
Alternatively, you can express it as:
$$
m = 3f
$$

**Final Equation:**
$$
f = \frac{1}{3} \, m
$$

This equation shows that the number of faces Esther paints is directly proportional to the time she spends painting, with each face taking 3 minutes.

**Answer:**  
A linear equation showing f equals one third of m:
 f = (1⁄3) · m
The number of faces Esther paints is one-third of the time she spends, so $$ f = \frac{1}{3}m $$.

Esther the Clown does face painting at the city carnival. She paints 7 faces every 21 minutes and spends the same amount of time painting each face. Write an equation that relates \( f \), the number of faces she paints, and \( m \), the time she spends painting in minutes.

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