Work Problems
Completion requirements
Work Problems
Work problems involve two or more people or things working together to complete a task in a certain amount of time. A formula based on how much time each individual could complete the task on their own can be developed. A general formula that will help solve these problems when two are working together is:
\[\frac{1}{{{\rm{time \thinspace taken\thinspace by \thinspace }}A}} + \frac{1}{{{\rm{time \thinspace taken \thinspace by\thinspace }}B{\rm{ }}}} = \frac{1}{{{\rm{time\thinspace taken\thinspace by\thinspace }}\thinspace A\thinspace {\rm{ and }}\thinspace B\thinspace {\rm{ together}}}}\]
The formula can be extended for more people or things. For example, if three people are working together, the formula would be amended to:
\[\frac{1}{{{\rm{time\thinspace taken\thinspace by \thinspace}}A}} + \frac{1}{{{\rm{time \thinspace taken \thinspace by \thinspace}}B{\rm{ }}}} + \frac{1}{{{\rm{time\thinspace taken\thinspace by \thinspace }}C{\rm{ }}}} = \frac{1}{{{\rm{time\thinspace taken\thinspace by\thinspace }}A,\thinspace B,{\rm{ \thinspace and \thinspace }}C{\rm{ \thinspace together}}}}\]