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Mia paints interior walls at a rate of

12(m^(2))/((h))". "
At what rate does Mia paint in

(cm^(2))/(min)" ? "

(cm^(2))/(min)

Mia paints interior walls at a rate of $12 \frac{\mathrm{m}^{2}}{\mathrm{~h}}$ . $\newline$ At what rate does Mia paint in $\frac{\mathrm{cm}^{2}}{\min }$ ? $\newline$ $\square$ $\frac{\mathrm{cm}^{2}}{\min }$

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Convert rates and measurements: customary units

Full solution

Q. Mia paints interior walls at a rate of

12 \frac{\mathrm{m}^{2}}{\mathrm{~h}}

.

\newline

At what rate does Mia paint in

\frac{\mathrm{cm}^{2}}{\min }

?

\newline

\square

\frac{\mathrm{cm}^{2}}{\min }

Convert units: To convert the rate from square meters per hour to square centimeters per minute, we need to know the conversion factors between meters and centimeters, and between hours and minutes. There are $100$ centimeters in a meter, and there are $60$ minutes in an hour.
Convert square meters to square centimeters: First, we convert square meters to square centimeters. Since there are $100$ centimeters in a meter, there are $100^2 = 10,000$ square centimeters in a square meter.
Multiply by conversion factor: Now, we multiply Mia's rate by the conversion factor from square meters to square centimeters. This gives us $12 \, \text{m}^2/\text{h} \times 10,000 \, \text{cm}^2/\text{m}^2 = 120,000 \, \text{cm}^2/\text{h}$ .
Convert hours to minutes: Next, we convert hours to minutes. Since there are $60$ minutes in an hour, we divide Mia's rate by $60$ to find the rate per minute.
Divide by $60$ : Dividing the rate in square centimeters per hour by $60$ gives us $120,000 \, \text{cm}^2/\text{h} \div 60 \, \text{min}/\text{h} = 2,000 \, \text{cm}^2/\text{min}.$
Calculate final rate: Therefore, Mia paints at a rate of $2,000$ square centimeters per minute.

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