One person does a job in 3 hours and another in 11 hours. How long together?
Working together they take 33/14 hours (about 2.3571429 hours, or 2 h 21 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/3 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 14/33 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 3 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{3} + \frac{1}{11} = \frac{1}{t}\ \Rightarrow\ t = \frac{33}{14} \]
\[ \frac{1}{3} + \frac{1}{11} = \frac{11 + 3}{33} = \frac{14}{33} \]
\[ t = \frac{33}{14} = \frac{33}{14} \approx 2.3571429\text{ hours} \]Questions
How long do they take together?
Working together they take 33/14 hours (about 2.3571429 hours, or 2 h 21 min).