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Betty paints twice as fast as Dan. Working together, Dan and Betty can paint 2, 400 square feet in 4 hours. Another employee, Sue, joined their painting team. Working together, Dan, Betty, and Sue can paint 3, 600 square feet in 3 hours. If Sue works alone, how many square feet can she paint in 4 hours and 27 minutes? a 600 square feet b 1, 570 square feet c 1, 700 square feet d 2, 530 square feet e 2, 670 square feet

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Answer:

2670 square feet. Option e.

Step-by-step explanation:

Dan and Betty can paint 2,400 square feet in 4 hours.

They can paint in one hour [tex]\frac{2400}{4}[/tex] = 600 square feet.

Since given that Betty paints twice as fast as Dan. Let us take an equation:

Let Betty = B, Dan = D and Sue = S

B = 2D

4(B+D) = 2400

4B + 4D = 2400

12D = 2400

D = 200 sq. ft.

B = 2D = 400 sq. ft.

Therefore, Dan can paint 200 square feet in 1 hour and Betty paints twice 400 square feet in 1 hour.

Now given three of them can paint 3,600 square feet in 3 hours.

3( B+D+S) = 3600

3B + 3D + 3S = 3600

3(400) + 3(200) + 3(S) = 3600

1200 + 600 + 3S = 3600

S = 600 Sq. ft.

Sue can paint 600 square feet in one hour.

So sue can paint in 4 hours and 27 minutes.

[tex](\frac{4+27}{60})[/tex] × 600

= 2670 square feet. Option e.

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