SOLUTION: Aris can paint a room in 5 ½ hours. His brother can do the same job in 7 ½ hours. How long will it take them to paint the room together?

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Question 767617: Aris can paint a room in 5 ½ hours. His brother can do the same job in 7 ½ hours. How long will it take them to paint the room together?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Aris can paint a room in 5 ½ hours.
His brother can do the same job in 7 ½ hours.
How long will it take them to paint the room together?
:
Let t = time required when working together
:
Let the completed job = 1, each will do a fraction of the job,
the two fractions add up to one
:
t%2F5.5 + t%2F7.5 = 1
Multiply by 55*75, 4125; Gets rid of the decimals and the denominators, results:
750t + 550t = 4125
1300t = 4125
t = 4125/1300
t = 3.173 hrs,working together
:
:
Check this
3.173%2F5.5 + 3.173%2F7.5 =
.577 + .423 = 1; confirms our solution