One person does a job in 6 hours and another in 12 hours. How long together?
Working together they take 4 hours.
How to work it out
- 1
Think in rates: in one hour the first does 1/6 of the job and the second does 1/12.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 18/72 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 6 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{6} + \frac{1}{12} = \frac{1}{t}\ \Rightarrow\ t = 4 \]
\[ \frac{1}{6} + \frac{1}{12} = \frac{12 + 6}{72} = \frac{18}{72} \]
\[ t = \frac{72}{18} = 4 \approx 4\text{ hours} \]Questions
How long do they take together?
Working together they take 4 hours.