Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 4 hours to paint a wall with dimensions a and c. He takes 2 hours to paint a wall with dimensions b and c and 6 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?  Choices:
A) 18 cubic meters B) 24 cubic meters C) 36 cubic meters D) 30 cubic meters E) It can’t be determined.
Time to paint each wall as given in problem:   A36 cubic meters = 4 hours   B36 cubic meters = 2 hours   AB = 6 hours   Since he works at constant rate and it takes him twice as long to paint A36 cubic meters compared to B36 cubic meters   A36 cubic meters=2B36 cubic meters   Plug in 6 for A and you find that B=3   Since painting AB takes 3 times as long compared to B36 cubic meters,   AB=3B36 cubic meters   Plug in 6 for A and 3 for B and you find that 36 cubic meters=2   A*B*36 cubic meters=6*3*2= 
<gadget id="calculator">6*3*2</gadget>
<output>36</output>
36 cubic meters   Answer: 36 cubic meters
<result>C</result>
Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 4 hours to paint a wall with dimensions a and c. He takes 2 hours to paint a wall with dimensions b and c and 6 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?