Question 226895
Tom and Jack paint a house.
 Working together they can paint the house in 2/3 of the time it takes Tom.
 Jack takes 6 hours to paint alone. How long does it take Tom to paint alone>?
:
Let t = time taken by Tom alone
then
{{{2/3}}}t = time working together
:
Let the completed job = 1
:
The shared work equation:
{{{((2/3)t)/t}}} + {{{((2/3)t)/6}}} = 1
Cancel t, and 2 into 6;
{{{2/3}}} + {{{((1/3)t)/3}}} = 1
Multiply equation by 3, results
2 + {{{(1/3)t}}} = 3
:
Multiply equation by 3 again
3(2) + t = 3(3)
6 + t = 9
t = 9 - 6
t = 3 hrs is Tom's time alone
:
:
Check solution:
(2/3)*3 = 2 hrs working together
{{{2/3}}} + {{{2/6}}} = 1