Joe is painting a rectangular room whose dimensions are given by a, b

Question

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.

Kudos for a correct solution.

A. 18 cubic meters
B. 24 cubic meters
C. 30 cubic meters 
D. 36 cubic meters
E. It can’t be determined.

Kudos for a correct  solution .

balamoon · Accepted Answer

Solution -

Given that Joe works at a constant rate, the area painted in one hour is the same.

Wall a and c has area ac took 8 hours to paint. Joe paints in one hour is ac/8.
Wall b and c has area bc took 4 hours to paint. Joe paints in one hour is bc/4.
Wall a and b has area ab took 12 hours to paint. Joe paints in one hour is ab/12.

So ac/8 = bc/4 = ab/12.

Since a = 6, bc/4 = 6b/12 --> c = 4 * 6 / 12 = 2

Substitute a = 6 and c = 2 in ac/8 = bc/4 --> b = 3

The volume of the room is abc = 6*3*2 = 36 cubic meters.

twilliamson88 · Answer

ac = 8 
ab = 12
bc = 4

ac = 2bc
divide c from both sides since we know it's non-zero
a=2b
a = 6 so b = 6/2

ab=3bc
6*3 = 3*3*c
divide both sides by 3*3
2=c

V=b*w*h so 2*3*6

kasinowr · Answer

Time to paint each wall as given in problem:

AC = 8 hours
BC = 4 hours
AB = 12 hours

Since he works at constant rate and it takes him twice as long to paint AC compared to BC
AC=2BC
Plug in 6 for A and you find that B=3

Since painting AB takes 3 times as long compared to BC,
AB=3BC
Plug in 6 for A and 3 for B and you find that C=2

A*B*C=6*3*2=36 cubic meters

Answer: D

JJo · Answer

Let r be the rate.
From given data, r=ac/8 = bc/4 = ab/12
putting a=6, r= 3c/4 = bc/4 = b/2
taking 1st 2 item from above equalities:
3c/4 = bc/4
b=3

hence, r = b/2 -->3/2
r=3/2 = 3c/4
hence, c=2

vol. abc = 6*3*2 = 36

Ans. D. 36 cubic meters

VenoMfTw · Answer

I will go with Option (D)

(a * c) sq .units = 8 hours to complete
(b * c) sq .units = 4 hours to complete
(a * b) sq .units = 12 hours to complete --> Since ceiling will have same dimensions as that of the base.

(a * c) sq .units = 2 * (b*c) sq units {Time taken to paint a*c sq units will be twice that of the time taken to paint the wall of b*c sq units)
given a=6, sub in the above equation
6c = 2bc => b = 3

Similarly 
a*b = 3*b*c 
6*b = 3*b*c 
c=2

Thus a=6 units , b=3units and c= 2units
Thus volume = abc = 36 cu units

Option D

Bunuel · Answer

800score Official Solution:

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.

So the correct answer is choice (D).

mvictor · Answer

wow, a very difficult one!

bumpbot · Answer

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Joe is painting a rectangular room whose dimensions are given by a, b

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