Finds how many days two people take together, from how long each takes alone. Taking the whole job as 1, the amounts each does in a day are added, and the total is inverted.
Two people each know how long the job takes them alone. To find how long it takes them together, take the whole job as 1, add what each does in a day, and invert the total.
is the days A takes alone, the days B takes alone and the days the two take together. The daily shares and are shown as well.
A takes 6 days alone and B takes 12. In a day A does of the job and B does , so together they do . A quarter of the job a day finishes it in days.
The answer is neither 18 days, the two added, nor 9 days, their average. What can be added is the work done in a day, not the days themselves. Days and work rates are reciprocals, so each is turned into a daily share first.
The answer always comes out shorter than the faster person takes alone. Here that is 4 days against the 6 days A takes.
Both figures must be positive. A job taking 0 days gives no daily share to work with.
The two are assumed to work at their usual pace without getting in each other's way.