One person does a job in 3 hours and another in 12 hours. How long together?
Working together they take 12/5 hours (about 2.4 hours, or 2 h 24 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 1/12.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 15/36 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
\[ \frac{1}{3} + \frac{1}{12} = \frac{1}{t}\ \Rightarrow\ t = \frac{12}{5} \]
\[ \frac{1}{3} + \frac{1}{12} = \frac{12 + 3}{36} = \frac{15}{36} \]
\[ t = \frac{36}{15} = \frac{12}{5} \approx 2.4\text{ hours} \]Questions
How long do they take together?
Working together they take 12/5 hours (about 2.4 hours, or 2 h 24 min).