Q:

A master painter can paint 110 square yards of surface area with a roller in 1 hour, while his apprentice can paint 85 square feet of surface area per hour with a brush . Together they are painting a building with a surface area of 5100 square feet. After painting for 4. 1/4 hours , the master painter lets the apprentice Finnish the job. Approximately how long will it take the apprentice to complete the project using a brush

Accepted Solution

A:
The apprentice needs 6.25 hours to complete the job using the brushSolution:Given, A master painter can paint 110 square yards of surface area with a roller in 1 hour[tex]\text { Then, his rate of painting }=110 \text { yard }^{2}[/tex]We know that 1 yard = 3 feet[tex]=110 \times(1 \text { yard })^{2}=110 \times(3 \text { feet })^{2}=110 \times 9 \text { feet }^{2}=990 \text { square feet. }[/tex]While his apprentice can paint 85 square feet of surface area per hour with a brush Together they are painting a building with a surface area of 5100 square feet.After painting for [tex]4\frac{1}{4}[/tex] hours , the master painter lets the apprentice Finish the job.  Now, they worked for [tex]4\frac{1}{4}[/tex] hours  Then, area painted = area painted by master + area painted by apprentice [tex]\text { Area painted }=990 \text { square feet per hour } \times 4 \frac{1}{4} \text { hours }+85 \text { square feet per hour } \times 4 \frac{1}{4} \text { hours }[/tex][tex]\text { Area painted }=990 \times \frac{4 \times 4+1}{4}+85 \times \frac{4 \times 4+1}{4}[/tex][tex]\begin{array}{l}{\text { Area painted }=990 \times \frac{17}{4}+85 \times \frac{17}{4}=(990+85) \times \frac{17}{4}} \\\\ {\text { Area painted }=1075 \times \frac{17}{4}=4568.75 \text { square feet. }}\end{array}[/tex]Now, the remaining area to be painted = total area – painted area  Area to be painted = 5100 – 4568.75 = 531.25 So, apprentice has to paint 531.25 square feet alone.[tex]\text { Then, time required }=\frac{\text { area to be painted }}{\text { his rate of painting }}[/tex][tex]=\frac{531.25}{85}=6.25[/tex]Hence, the apprentice needs 6.25 hours to complete the job