One person does a job in 7 hours and another in 12 hours. How long together?
Working together they take 84/19 hours (about 4.4210526 hours, or 4 h 25 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/7 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 19/84 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 7 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{7} + \frac{1}{12} = \frac{1}{t}\ \Rightarrow\ t = \frac{84}{19} \]
\[ \frac{1}{7} + \frac{1}{12} = \frac{12 + 7}{84} = \frac{19}{84} \]
\[ t = \frac{84}{19} = \frac{84}{19} \approx 4.4210526\text{ hours} \]Questions
How long do they take together?
Working together they take 84/19 hours (about 4.4210526 hours, or 4 h 25 min).