Question 1174933
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First a formal algebraic solution....<br>
x = # of hours the faster person takes to do the job
3x = # of hours the slower person takes<br>
1/x = fraction of the job the faster person does in 1 hour
1/3x = fraction of the job the slower person does in 1 hour
1/3 = fraction of the job they do together in 1 hour<br>
Then<br>
{{{1/x + 1/(3x) = 1/3}}}<br>
Multiply by the LCD 3x to clear fractions<br>
{{{3+1 = x}}}
{{{x = 4}}}<br>
The faster person takes x=4 hours to do the job alone, so the slower person takes 3x=12 hours.<br>
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Informally, using logical reasoning....<br>
Since the faster person works 3 times as fast as the slower person, when working together the faster person does 3/4 of the job and the slower person does 1/4.<br>
Working together, it takes the two of them 3 hours to do the job.<br>
So in 3 hours the slower worker does 1/4 of the job; that means it would take him 4*3=12 hours to do the job alone.<br>