Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her own.

Question

mathmate · Answer

Again, reduce everything to how much they can work in one hour.
Let 
C=number of hours Carl takes to do the job
J=number of hours Jennifer takes to do the job
Then
"Carl can paint a room 3 hours faster than Jennifer can."
means
1/C-1/J = 1/3    ...........(finishes three hours faster)
" If they work together, they can complete the job in 2 hours."
means
1/C+1/J=1/2

This looks like a difficult equation to solve, but whenever you have the special case like
a+b=S
a-b=D
Then a=(S+D)/2, and b=(S-D)/2.

Applying the shortcut,
1/C=(1/2+1/3)/2=(5/6)/2=5/12
1/J=(1/2-1/3)/2=1/12

So Jennifer will take 1/(1/12)=12 hours to finish the job.
Carl will take 1/(5/12)=2.4 hours to finish the job.
check: 5/12-1/12=4/12=1/3   .... yes, each hour Carl will finish 1/3 more than Jenn.
5/12+1/12=6/12=1/2......yes, the two work together will finish in two hours.

monteskellie · Answer

I believe it is 6 but not sure

mathmate · Answer

Take the time to read through my solution and understand every step.
If you have questions, feel free to ask.
I or someone else will be pleased to help you!

monteskellie · Answer

I am still a little confused by I will try to figure it out

welshfella · Answer

you can also find it by solving  1 / (3 - x) + 1/x = 1/2

where x is the  number of hours taken by jennifer

welshfella · Answer

sorry  thats not correct   it should be  

1 / (x - 3) + 1/x  = 1/2

welshfella · Answer

this will give you 2 values of x but only one is possible.