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

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

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

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

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).

wow, a very difficult one!

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