To find out how many square feet Stefanie can paint in one hour, we need to first determine her painting rate based on the information given.
Stefanie can paint \( 12 \frac{2}{3} \) square feet in \( \frac{3}{5} \) of an hour. We can convert \( 12 \frac{2}{3} \) into an improper fraction:
\[ 12 \frac{2}{3} = 12 + \frac{2}{3} = \frac{36}{3} + \frac{2}{3} = \frac{38}{3} \text{ square feet.} \]
Now, we can find her painting rate by dividing the area she can paint by the time it takes:
\[ \text{Rate} = \frac{\text{Area}}{\text{Time}} = \frac{\frac{38}{3} \text{ square feet}}{\frac{3}{5} \text{ hour}}. \]
To divide by a fraction, we can multiply by the reciprocal:
\[ \text{Rate} = \frac{38}{3} \times \frac{5}{3} = \frac{38 \times 5}{3 \times 3} = \frac{190}{9} \text{ square feet per hour.} \]
Now to express \( \frac{190}{9} \) square feet per hour in a more understandable form, we can convert it to a mixed number:
\[ 190 \div 9 = 21 \text{ (the whole number part)}, \] with a remainder of \( 1 \) (since \( 9 \times 21 = 189 \)).
Thus, we can write:
\[ \frac{190}{9} = 21 \frac{1}{9} \text{ square feet per hour.} \]
Therefore, Stefanie can paint approximately \( 21 \frac{1}{9} \) square feet in one hour.
5 answers