SOLUTION: Hannah can paint a room in 10 hours. Destiny can paint the same room in 8 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together.Ty

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Question 1151378: Hannah can paint a room in 10 hours. Destiny can paint the same room in 8 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together.Type your answer as a reduced fraction.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52872) About Me  (Show Source):
You can put this solution on YOUR website!
.

Hannah makes  1%2F10  of the job per hour.


Destiny makes  1%2F8  of the job per hour.


Working together, the two make  1%2F10 + 1%2F8 of the job per hour,

    which is  1%2F10 + 1%2F8 = 4%2F40+%2B+5%2F40 = 9%2F40  of the job per hour.



It means that Hannah and Destiny will complete the job in  40%2F9 = 44%2F9 hours working together.    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(13208) About Me  (Show Source):
You can put this solution on YOUR website!


Here an alternative to the standard algebraic solution method shown by the other tutor.

Consider the least common multiple of the two given times; the LCM of 8 hours and 10 hours is 40 hours.

Hannah, taking 10 hours to paint a room, could paint 40/10=4 rooms in 40 hours; Destiny, taking 8 hours to paint a room, could paint 40/8=5 rooms in 40 hours.

So together in 40 hours the two of them together could paint 4+5=9 rooms.

And that means the number of hours it would take them together to paint the one room is 40/9.

ANSWER: 40/9 hours; or 4 4/9 hours