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

Algebra ->  Rate-of-work-word-problems -> 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      Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!


Using a standard algebraic approach....

x = hours John would take to do the job alone

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:

1%2F3%2B1%2Fx=1%2F2

Multiply through by the least common denominator, 6x:

2x%2B6=3x
x=6

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.


Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.