SOLUTION: John can paint a room three times as fast as Mary. Together, they can paint the same room in 1.5 hours. How long does it take each one working alone to paint that room?

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Question 1137621: John can paint a room three times as fast as Mary. Together, they can paint
the same room in 1.5 hours. How long does it take each one working alone
to paint that room?

Answer by ikleyn(52903)   (Show Source): You can put this solution on YOUR website!
.
John works as effectively as three workers equivalent to Mary work.


So, when John and Mary work together,  they work as effectively as 4 workers like Mary work.


Thus you can reformulate the given part in this way:



    4 workers equivalent to Mary can paint the room in 1.5 hours.



Then it is clear that Mary alone can do this job in 4*1.5 = 6 hours.


Since John can do it in 3 times faster, he needs only 2 hours.


Answer.  John needs 2 hours to complete the job working alone.

Solved.   //   Mentally,  without using equations, leaning on the common sense only.

-----------------

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.


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