Question 496727
If Tom, George and Mario work together, they can paint a 600 ft2 room in 4 hours.
  When only George and Mario work together, it takes 8 hours to paint the room.
  Tom and George, working together, take 6 hours to paint the room.
  How long would it take Tom to paint the room alone? 
:
Let the completed job = 1, (a painted room)
Let t = To alone
let g = George alone
let m = Mario alone
:
Write a shared work equation for each statement:
:
 "Tom, George and Mario work together, they can paint a room in 4 hours."
{{{4/t}}} + {{{4/g}}} + {{{4/m)}}} = 1
:
"When only George and Mario work together, it takes 8 hours to paint the room."
{{{8/g}}} + {{{8/m)}}} = 1
:
"Tom and George, working together, take 6 hours to paint the room."
{{{6/t}}} + {{{6/g)}}} = 1
:
Use elimination here, multiply the 1st equation by 6, the 2nd equation by 3
{{{24/t}}} + {{{24/g}}} + {{{24/m)}}} = 6
{{{0/t}}} +  {{{24/g}}} + {{{24/m)}}} = 3
-------------------------------------------subtraction eliminates g and m
{{{24/t}}} + 0 + 0 = 3
3t = 24
t = 24/3
t = 8 hrs for Tom working alone