One person does a job in 9 hours and another in 12 hours. How long together?
Working together they take 36/7 hours (about 5.1428571 hours, or 5 h 9 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/9 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 21/108 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 9 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{9} + \frac{1}{12} = \frac{1}{t}\ \Rightarrow\ t = \frac{36}{7} \]
\[ \frac{1}{9} + \frac{1}{12} = \frac{12 + 9}{108} = \frac{21}{108} \]
\[ t = \frac{108}{21} = \frac{36}{7} \approx 5.1428571\text{ hours} \]Questions
How long do they take together?
Working together they take 36/7 hours (about 5.1428571 hours, or 5 h 9 min).