One person does a job in 3 hours and another in 6 hours. How long together?
Working together they take 2 hours.
How to work it out
- 1
Think in rates: in one hour the first does 1/3 of the job and the second does 1/6.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 9/18 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
\[ \frac{1}{3} + \frac{1}{6} = \frac{1}{t}\ \Rightarrow\ t = 2 \]
\[ \frac{1}{3} + \frac{1}{6} = \frac{6 + 3}{18} = \frac{9}{18} \]
\[ t = \frac{18}{9} = 2 \approx 2\text{ hours} \]Questions
How long do they take together?
Working together they take 2 hours.