It takes 28 hours for John to paint four walls and the ceiling of a ro

another one, you don't stop lol....

1st) When he paints the 4 Walls and Ceiling in 28 hours, he paints the following Surface Area of the Room:

L*H + W*H + L*H + W*H + (Ceiling of Dimensions L*W)


2nd) Since we are given the Volume = 800 and the Ceiling Height = 8, we can determine the Surface Area of the Ceiling = L*W

L*W*H = 800

L*W*8 = 800

L*W = 100 = Surface Area of Ceiling


3rd) Calculate his Constant Painting Rate based on what he finished in 28 hours


His Constant Work Rate = (1/4) ft/min

Work Rate = (Work Completed) / (Time Taken)


He Painted the 4 Walls and Ceiling in 28 hours (or 1,680 minutes):

Work Completed = L*H + W*H + L*H + W*H + Ceiling Area of 100

Work Completed = 8L + 8W + 8L + 8W + 100

Work Completed = 16 * (L +W) + 100

Time needed to Complete this Work = 1, 680 minutes



Now we can Set this Rate of Work EQUAL to the Given Rate of Work = (1/4) ft/min


1/4 = [ 16 * (L + W) + 100 ] / 1,680


---cross-multiplying---

1, 680 = 64 * (L + W) + 400

1,280 = 64 * (L + W)

L + W = 1, 280 / 64 ----- equation 1



The Question asks us how long it will take to Paint the JUST the 4 Walls and NOT the Ceiling:

Time = (Work) / (Rate)

The Surface Area WORK of the 4 Walls that needs to be completed = 8L + 8W + 8L + 8W = 16 * (L + W)

His Constant Rate of work is given by = (1/4) ft/min


Time in minutes = [ 16 * (L + W) ] / (1/4)


Substitute in --- equation 1 ---- (L + W) = 1, 280 / 64


Time in minutes = [ 16 * (1, 280 / 64) ] / (1/4)

---simplifying----

Time = (1, 280 * 4) / 4 = 1,280 minutes


Converting to Hours ---- 1,280 minutes / 60 minutes = 21 + (20/60)


or

21 hours and 20 minutes

Answer -A-