SOLUTION: Mark and Luke can paint a room together in 4 hours if it takes mark 9 hours to paint by himself how long will it take luke to paint by himself?

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Question 1156528: Mark and Luke can paint a room together in 4 hours if it takes mark 9 hours to paint by himself how long will it take luke to paint by himself?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.

Working together, they make    of the job per hour.


Working alone, Mark makes    of the job per hour.


Hence, Luke makes   -  =  -  =  of the job per hour.


It means that Luke will complete the job in  =  hours = 7 hours and 12 minutes.    ANSWER

Solved.

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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.


Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Here are a couple of alternatives to the standard solution method shown by tutor @ikleyn.

Try using all three methods and find the one that works best for you....

(1) Together they take 4 hours to do the job; Mark alone takes 9 hours. So in the 4 hours that they work together, Mark does 4/9 of the job.
That means Luke in those 4 hours does 5/9 of the job.
So the amount of time it takes Luke to do the job alone is 4*(9/5) = 36/5 = 7.2 hours.

As an alternative for the last step by this method, note that Luke works 5/4 as fast as Mark, so the amount of time it takes him alone is 4/5 of the time it takes Mark alone: 9*(4/5) = 36/5.

(2) Consider the least common multiple of the two given times, which is 36 hours.
In 36 hours, Mark could do the job 36/4 = 9 times, and together they could do it 36/9 = 4 times.
That means in 36 hours Luke could do the job 9-4 = 5 times.
So the amount of time Luke would take to do the job alone is 36/5 = 7.2 hours.
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