SOLUTION: Last year Michael painted his room in 3 hours. This year Michael and John were able to paint the room together in 2 hours. How long would it have taken John to paint the room worki
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Question 1185495: Last year Michael painted his room in 3 hours. This year Michael and John were able to paint the room together in 2 hours. How long would it have taken John to paint the room working alone? Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
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:
Multiply through by the least common denominator, 6x:
ANSWER: John alone would take x=6 hours to do the job alone.
You should understand how to set up and solve the problem using formal algebra.
But solving a problem like this informally, using logical analysis and simple mental arithmetic, is valuable brain exercise.
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.