One person does a job in 11 hours and another in 12 hours. How long together?
Working together they take 132/23 hours (about 5.7391304 hours, or 5 h 44 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/11 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 23/132 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 11 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{11} + \frac{1}{12} = \frac{1}{t}\ \Rightarrow\ t = \frac{132}{23} \]
\[ \frac{1}{11} + \frac{1}{12} = \frac{12 + 11}{132} = \frac{23}{132} \]
\[ t = \frac{132}{23} = \frac{132}{23} \approx 5.7391304\text{ hours} \]Questions
How long do they take together?
Working together they take 132/23 hours (about 5.7391304 hours, or 5 h 44 min).