Somebody who takes six hours does a sixth of the job each hour. Rates are what add when two people work together, which is why the answer is never the average of the two times.
One painter takes 6 hours and another takes 3 hours. How long together?
The first does a sixth an hour, the second a third.
Together that is a sixth plus a third, which is a half an hour.
So the whole job takes 2 hours.
The answer is 2 hours.
Where students go wrong
Averaging the two times. Six hours and three hours does not give four and a half: two people are always faster than either alone, so the answer has to be under the smaller of the two.
Also called work rate problems, working together problems, pipes filling a tank or combined work.
Questions about these worksheets
Yes. Every work word problems sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the work word problems questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Averaging the two times. Six hours and three hours does not give four and a half: two people are always faster than either alone, so the answer has to be under the smaller of the two.