Time and Work

Formula / Rule

Time and Work

Topic

Time, Work & Speed

Formula

If A completes work in $n$ days, A does $\frac{1}{n}$ work per day.

Combined rate: A and B together do $\left(\frac{1}{a} + \frac{1}{b}\right)$ work per day.

Time taken together = $\frac{a \times b}{a + b}$

Efficiency ratio: If A is $k$ times as efficient as B, A takes $\frac{1}{k}$ the time B takes to complete the work.

Pipes: A filling pipe adds volume ($+$); an emptying pipe (leak) subtracts volume ($-$).

When to Use

Problems involving work done by individuals or groups, and pipe and cistern problems.

Worked Example

Q: A completes work in $10$ days, B in $15$ days. How many days will they take together?

$\text{Time together} = \frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6 \text{ days}$