One person does a job in 10 hours and another in 12 hours. How long together?
Working together they take 60/11 hours (about 5.4545455 hours, or 5 h 27 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/10 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 22/120 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 10 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{10} + \frac{1}{12} = \frac{1}{t}\ \Rightarrow\ t = \frac{60}{11} \]
\[ \frac{1}{10} + \frac{1}{12} = \frac{12 + 10}{120} = \frac{22}{120} \]
\[ t = \frac{120}{22} = \frac{60}{11} \approx 5.4545455\text{ hours} \]Questions
How long do they take together?
Working together they take 60/11 hours (about 5.4545455 hours, or 5 h 27 min).