SOLUTION: Hello, can you help me solve this problem? Please? Allan and Andrew can paint a room in 3hrs. It takes Allan 7 hrs to do this alone. Without Allan, how long will it take Andrew

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Hello, can you help me solve this problem? Please? Allan and Andrew can paint a room in 3hrs. It takes Allan 7 hrs to do this alone. Without Allan, how long will it take Andrew       Log On


   



Question 1098169: Hello, can you help me solve this problem? Please?
Allan and Andrew can paint a room in 3hrs. It takes Allan 7 hrs to do this alone. Without Allan, how long will it take Andrew to paint the same room?
Thank you

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx%2B1%2F7=1%2F3
-
1%2Fx=1%2F3-1%2F7
1%2Fx=7%2F21-3%2F21=4%2F21
x=21%2F4
highlight%28x=5%261%2F4%29
5 hours 15 minutes

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Their combined rate of work is 1%2F3 of the job per hour.

Allan's individual rate of work is 1%2F7 of the job per hour.


Hence, Andrew's individual rate of work is the difference 1%2F3 - 1%2F7 of the job per hour.


1%2F3 - 1%2F7 = 7%2F21 - 3%2F21 = 4%2F21.


Thus Andrew's individual rate of work is  4%2F21 of the job per hour.


Hence, it will take  21%2F4 hours = 5 hours and 15 minutes for Andrew to complete the entire job working alone.

Solved.

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It is a 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.