Question 1185495
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Using a standard algebraic approach....<br>
x = hours John would take to do the job alone<br>
The fraction Michael does in 1 hour is 1/3; the fraction John does in 1 hour is 1/x; together, the fraction they do in 1 hour is 1/2:<br>
{{{1/3+1/x=1/2}}}<br>
Multiply through by the least common denominator, 6x:<br>
{{{2x+6=3x}}}
{{{x=6}}}<br>
ANSWER: John alone would take x=6 hours to do the job alone.<br>
You should understand how to set up and solve the problem using formal algebra.<br>
But solving a problem like this informally, using logical analysis and simple mental arithmetic, is valuable brain exercise.<br>
In the 2 hours that it takes the two together to paint the room, Michael does 2/3 of the job, because he can paint the whole room alone in 3 hours.
That means in 2 hours John does the other 1/3 of the job.
And that means the number of hours it would take him to point the whole room alone (3/3 of the job) would be 3*2=6.<br>