if aaron can do a job in 8 days and ben can do the same job in 12 days how long does it take in hours for the two men working?

AARON alone = 8 days

AARON ALONE in 1 DAY = 1/8 of the work

BEN ALONE in 1 DAY = 1/12 of the work

TOGETHER IN 1 DAY = 1/8+1/12 = 3/24+ 2/24 = 5/24 of the work

TOGETHER they will finish the work in 24/5 days OR 4.8 days ANSWER

1/8 + 1/12 = 1/x 3/24 + 2/24 = 5/24 = 1/x x=24/5=4.8 days

Let the work is as big as W=24A.

Then Aaron can do as much as W/8 = 3A daily while Ben can do W/12 = 2A. They can do 3A+2A=5A together.

So the time needed is (24A)/(5A) = 4.8 days

{Why we have taken 24A? Because of it is the LCM for 8, 12. You can use 8*12=96 instead.}

First use the standard formula, which is the

product of the two times divided by the sum.

So we get 96/20 = 4.8 . . . days, which equates

to 115.2 hours

If aaron can do a job in 8 days and ben can do the same job in 12 days how long does it take in hours for the two men working?

Aaron can do the job in 8 days ----> in 1 day, Aaron does 1/8 of job
Ben can do the job in 12 days ----> in 1 day, Ben does 1/12 of job

Working together, in 1 day the can do 1/8 + 1/12 = 5/24 of job
So together, they work at a rate of (5/24) job/day

1 job / (5/24 job/day) = 24/5 days.

Now the question is not clear what they mean by "day"
It's ridiculous to think either man can work 8 or 12 full 24-hour days non-stop. And using a 24-hour day to measure a job that is strung out over several 8 or 10 hour days doesn't make much sense.

Because of this, I'm not too sure how to answer this question.
But assuming a 24-hour work day (!), it would take them:
24/5 days * 24 hours/day = 115.2 hours

The equation I use is:

work = rate * time

We can find the rates of the two people using "1" as work (since it's the same job):

w = rt
1 = r * 8 and 1 = r * 12
r = 1/8 and r = 1/12

When both are working together, the rates are added:

1/8 + 1/12
3/24 + 2/24
5/24

So how long does it take when both are working together:

w = rt
1 = (5/24)t
t = 24/5 days (4.8 days)

To get it in terms of hours, multiply by 24:

576/5 hours (115.2 hours)

1/(1/8+1/12) = ...

t/8+t/12=1

(3t+2t)/24=1

5t=24

t=24/5 d

t=4 days, 19 hours, 12 minutes