One person does a job in 12 hours and another in 12 hours. How long together?
Working together they take 6 hours.
How to work it out
- 1
Think in rates: in one hour the first does 1/12 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 24/144 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 12 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{12} + \frac{1}{12} = \frac{1}{t}\ \Rightarrow\ t = 6 \]
\[ \frac{1}{12} + \frac{1}{12} = \frac{12 + 12}{144} = \frac{24}{144} \]
\[ t = \frac{144}{24} = 6 \approx 6\text{ hours} \]Questions
How long do they take together?
Working together they take 6 hours.