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?
:
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/5.5}}} + {{{t/7.5}}} = 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
{{{3.173/5.5}}} + {{{3.173/7.5}}} = 
.577 + .423 = 1; confirms our solution