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

Algebra.Com
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(52873)   (Show Source): You can put this solution on YOUR website!
.

Hannah makes    of the job per hour.


Destiny makes    of the job per hour.


Working together, the two make   +  of the job per hour,

    which is   +  =  =   of the job per hour.



It means that Hannah and Destiny will complete the job in   =  hours working together.    ANSWER

Solved.

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

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)   (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
RELATED QUESTIONS

Hannah can paint a room in 8 hours. Destiny can paint the same room in 6 hours. How long... (answered by nerdybill)
Hannah can paint a room in 9 hours. Destiny can paint the same room in 12 hours. How long (answered by stanbon,josgarithmetic)
1. One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 8... (answered by Edwin McCravy)
Please help me and show all steps Rational Equations, Inequalities and Applications (answered by ikleyn)
rebecca can paint a room in 9 hours. Ryan can paint the same room in 8 hours. How long... (answered by Alan3354)
Ethan can paint a room in eleven hours. Victoria can paint the same room in twelve hours. (answered by ptaylor)
taylor can paint a room in twelve hours. Jennifer can paint the room in ten hours. How... (answered by nerdybill)
hannah can paint a room in 8hrs. Miley can paint it in 10hrs. working together, how many... (answered by Alan3354,scott8148)
If Norm and cliff together can paint a room in 4 hours, and Norm can paint the same room... (answered by edjones)