Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 8 hours to paint a wall with dimensions a and c. He takes 4 hours to paint a wall with dimensions b and c and 12 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 6, then what is the volume of the room?
A. 18 cubic meters B. 24 cubic meters C. 30 cubic meters D. 36 cubic meters E. It can’t be determined.
(D) This is a typical work problem with an addition, finding the volume. Start by finding the area of the two walls and the ceiling.
Wall 1 has the area ac, and it took 8 hours to paint it. So the area Joe paints in one hour is (ac)/8.
Wall 2 has area bc, and took 4 hours to paint. So the area Joe paints in one hour is (bc)/4.
The ceiling has the area ab, and it took 12 hours to paint it. So the area Joe paints in one hour is (ab)/12.
Since Joe is working at a constant rate, the area painted in one hour is the same. So (bc)/4 = (ab)/12 .
Since a = 6, (bc)/4 = (6b)/12 .
So c = 4 × 6 / 12 .
c = 2
(ac)/8 = (bc)/4, where a = 6 and c = 2. So (6 × 2)/8 = (b × 2)/4.
b = 3
This gives a = 6 meters, b = 3 meters, and c = 2 meters. The volume of the room is a × b × c = 6 × 3 × 2 = 36 cubic meters.
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