Work problems

If a person can complete a job in $t$ hours, their work rate is $\frac{1}{t}$ jobs per hour. When multiple workers combine their rates, the total rate is the sum of their individual rates. The time to complete the job together is the reciprocal of the total rate.

Important properties

• Work rate = $\frac{1}{\text{time to complete job}}$

• Combined rate = sum of individual rates

• Total time = $\frac{1}{\text{combined rate}}$

• If $A$ and $B$ can do a job in $a$ and $b$ hours, together they take $\frac{ab}{a+b}$ hours