One person does a job in 10 hours and another in 11 hours. How long together?
Working together they take 110/21 hours (about 5.2380952 hours, or 5 h 14 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 1/11.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 21/110 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
\[ \frac{1}{10} + \frac{1}{11} = \frac{1}{t}\ \Rightarrow\ t = \frac{110}{21} \]
\[ \frac{1}{10} + \frac{1}{11} = \frac{11 + 10}{110} = \frac{21}{110} \]
\[ t = \frac{110}{21} = \frac{110}{21} \approx 5.2380952\text{ hours} \]Questions
How long do they take together?
Working together they take 110/21 hours (about 5.2380952 hours, or 5 h 14 min).