Question 465706
Tom can paint a room in 5 hours; if he works with Tim, they can paint together the same room in 2 hours.
 How long does it take for Tim to paint the room by himself?
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Here is a simple and understandable method of doing these shared work problems
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Let t = Tim's time working alone
Let the completed job = 1
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Each man will do a fraction of the job; the two fractions must add up to 1 (a complete job)
:
{{{2/5}}} + {{{2/t}}} = 1
Multiply by 5t to clear the denominators, results
2t + 5(2) = 5t
2t + 10 = 5t
10 = 5t - 2t
10 = 3t
t = {{{10/3}}}
t = 3{{{1/3}}} hrs Tim working alone
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See if these two fractions add up to 1
2/5 + 2/3.33
.4 + .6 = 1