Question 950897
Andre and Eric have a home improvement business.
 They get a job to paint the living room of mrs. Jones.
 Andre can paint a room in 4 hours and Eric can paint a room in 12 hours.
 They decide to paint a room together to save time. How long does it take for the two of them to paint the room?
:
You are right, but here is an easy understandable way to do these "shared work" problems
let t = time required when they work together
let the completed job = 1 (a painted room)
:
Each will do a fraction of the job, the two fractions add up to
{{{t/4}}} + {{{t/12}}} = 1
multiply equation by a common multiple of the denominator
12*{{{t/4}}} + 12*{{{t/12}}} = 12
Cancel the denominators
3t + t = 12
4t = 12
t = 12/4
t = 3 hrs when working together
:
:
See if the two fraction in fact add up to 1 
{{{3/4}}} + {{{3/12}}} = 
{{{3/4}}} + {{{1/4}}} = 1