Sam can do a job in 3 hours, Bill can do the same job in 9 hours. How long does it take them to do the job together?

Question

I need the answer of how long it will take them to do it together

Answer 1

Sam can do a job in 3 hours, Bill can do the same job in 9 hours. How long does it take them to do the job together?

Now, if Sam works for 3 hours, then stops; then, Bill works for 9 hours, then stops, that's a total of 12 hours for 2 jobs, done serially (one after the other).

So, Sam working for 1.5 hours followed by Bill working for 4.5 hours gets the job done in 6 hours.

However, working together, they can complete a job quicker.

This is a simplified problem. I call the numbers used in this type of problem "magic numbers" because they make the calculations easy so you can concentrate on the procedure.

Please resist any shortcuts for now -- the goal is to learn the procedure.

First you should realize that rates may be in terms of "jobs per hour" or "hours per job." Therefore, units are important in solving this problem.

"How long will it take" is time; Let's cal that x. "the same job together" is one job. So, we add the parts of the job that each does in 1 hour:

(part of job done by Sam per hour) + (part of job done by Bill per hour) = (1 job) / (x hours)

1/3 + 1/9 = 1/x

3/9 + 1/9 = 1/x

4/9 = 1/x

x = 9/4

x = 2 1/4 hours

Check:

WORKING TOGETHER:

In (2 1/4 hours) Sam can do ((1 job) / (3 hours))*(2 1/4 hours)

(1/3)(9/4) jobs

3/4 job

In (2 1/4 hours) Bill can do ((1 job) / (9 hours))*(2 1/4 hours)

(1/9)(9/4 jobs

1/4 job

3/4 job + 1/4 job = 1 job ; they start at the same time and they complete at the same time

Answer 2

Well, they can do 2 jobs in 12 hours so , by ratio, they can do 1 job in 6 hours!