One person does a job in 6 hours and another in 9 hours. How long together?
Working together they take 18/5 hours (about 3.6 hours, or 3 h 36 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/6 of the job and the second does 1/9.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 15/54 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
\[ \frac{1}{6} + \frac{1}{9} = \frac{1}{t}\ \Rightarrow\ t = \frac{18}{5} \]
\[ \frac{1}{6} + \frac{1}{9} = \frac{9 + 6}{54} = \frac{15}{54} \]
\[ t = \frac{54}{15} = \frac{18}{5} \approx 3.6\text{ hours} \]Questions
How long do they take together?
Working together they take 18/5 hours (about 3.6 hours, or 3 h 36 min).