One person does a job in 11 hours and another in 11 hours. How long together?
Working together they take 11/2 hours (about 5.5 hours, or 5 h 30 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 1/11.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 22/121 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
\[ \frac{1}{11} + \frac{1}{11} = \frac{1}{t}\ \Rightarrow\ t = \frac{11}{2} \]
\[ \frac{1}{11} + \frac{1}{11} = \frac{11 + 11}{121} = \frac{22}{121} \]
\[ t = \frac{121}{22} = \frac{11}{2} \approx 5.5\text{ hours} \]Questions
How long do they take together?
Working together they take 11/2 hours (about 5.5 hours, or 5 h 30 min).