Algebra!!!!?

school at home: Algebra!!!!?
One Person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?

**Please check and show all your work

Answers and Views:

Answer by vekkus4
I think it works to set it up like this:

Person A works at 1/8 jobs/hour
Person B works at 1/12 jobs/hour

then if B works x hours and A works (x-2) hours
then the amount of work is
x * 1/12 + (x-2) * 1/8 = 1
x/12 + (x-2)/8 = 1
multiply through by common denominator 24
2x + 3(x-2) = 24
2x + 3x – 6 = 24
5x = 30

x = 6 person B works 6 hours, person A works 4 hours

check: 6/12 + 4/8 = 1/2 + 1/2 = 1.