word problem?

Question

Jill can do a job in 8 hours. John can do it in 12 hours. If Jill works 2 hours less than John, how many hours will it take them working together?

Answer 1

10 hours; 6 if they work simultaneously.
Jill works 4 hours, John works 6 hours.
Jill does 4/8 of the job in 4 hours, and John does 6/12 of the job in 6 hours.

Haha, the heck I'm wrong. If Jill does a job in 8 hours, and John does one in 12, then Jill does 1/8 job an hour and John does 1/12 job an hour.
How is that wrong?

Answer 2

The man above is wrong.

Anyway,

John = 1/12
Jill = 1/8

Now, John worked 2 hours more.

John in 2 hours + John work + Jill Work = 1
(2/12) + (x/12) + (x/8) = 1

You use 1 at the end because you want 100% of the work done.

Now you solve for x.

Answer 3

Since they are working together it should take them half the time. 6 hours should be the answer (John working 6 and Jill working 4)

Answer 4

T = (J - 2J/12)(J/2 + J/12) + 2
T = (12J - 2J)(6J + J) + 2
T = (10)(7) + 2 = 24/7
T ≈ 3.43 hr

Check:
10J/14 + 24J/84 =
J(60 + 24)/84 = J