Question

modeling real life you can sand \\(\frac{4}{9}\\) square yard of wood in \\(\frac{1}{2}\\) hour. how many square yards can you sand in 3.2 hours?\
\\(\circ\\) 2.8 square yards\
\\(\circ\\) 2.84 square yards\
\\(\circ\\) \\(2.\overline{84}\\) square yards\
\\(\circ\\) \\(2.\overline{84}\\) square yards

Explanation:

Step1: Find sanding rate per hour

Rate = $\frac{\text{Area}}{\text{Time}} = \frac{\frac{4}{9}}{\frac{1}{2}} = \frac{4}{9} \times 2 = \frac{8}{9}$ square yards/hour

Step2: Calculate area for 3.2 hours

First convert 3.2 to fraction: $3.2 = \frac{16}{5}$
Area = Rate $\times$ Time = $\frac{8}{9} \times \frac{16}{5} = \frac{128}{45}$

Step3: Convert to decimal

$\frac{128}{45} = 2.8\overline{4}$

Answer:

2.8$\overline{4}$ square yards