Question 198387
If John can paint a house in 6 hours. Mary can paint one in 4 hours
 and Sue can paint one in 2 hours, how long would it take them to paint
 a house if they worked together?
:
Let t = time required if they all work together
:
Let the completed job = 1
:
Each will paint a fraction of the house. All three fractions add up to 1
{{{t/6}}} + {{{t/4}}} + {{{t/2}}} = 1
Multiply by 12:
12*{{{t/6}}} + 12*{{{t/4}}} + 12*{{{t/2}}} = 12(1)
Cancel out the denominators; results:
2t + 3t + 6t = 12
:
11t = 12
t = {{{12/11}}}
t = 1.09 hrs or 1 hr + .09(60) = 5.45 min