Question

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

Answer 1

Explanation:

question: A master painter can paint 110 square yards of surface area with a roller in 1 hour, while his apprentice [a person who is learning] can paint 85 square feet of surface area per hour with a brush. The master painter asked his apprentice to paint a surface area of 5,100 square feet. The apprentice paints for 5.5 hours. After 5.5 hours, how many square feet does the apprentice have left to paint?

Select one:

A. 4,095.5 square feet

B. 4,495 square feet

C. 5015 square feet

D. 4632.5 square feet

Answer 2

The apprentice needs 6.25 hours to complete the job using the brush

Solution:

Given, A master painter can paint 110 square yards of surface area with a roller in 1 hour

`\text { Then, his rate of painting }=110 \text { yard }^(2)`

We know that 1 yard = 3 feet

`=110 *(1 \text { yard })^(2)=110 *(3 \text { feet })^(2)=110 * 9 \text { feet }^(2)=990 \text { square feet. }`

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 Finish the job.

Now, they worked for
`4(1)/(4)` hours

Then, area painted = area painted by master + area painted by apprentice

`\text { Area painted }=990 \text { square feet per hour } * 4 (1)/(4) \text { hours }+85 \text { square feet per hour } * 4 (1)/(4) \text { hours }`

`\text { Area painted }=990 * (4 * 4+1)/(4)+85 * (4 * 4+1)/(4)`

`\begin{array}{l}{\text { Area painted }=990 * (17)/(4)+85 * (17)/(4)=(990+85) * (17)/(4)} \\\\ {\text { Area painted }=1075 * (17)/(4)=4568.75 \text { square feet. }}\end{array}`

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.

`\text { Then, time required }=\frac{\text { area to be painted }}{\text { his rate of painting }}`

`=(531.25)/(85)=6.25`

Hence, the apprentice needs 6.25 hours to complete the job