One person does a job in 8 hours and another in 9 hours. How long together?
Working together they take 72/17 hours (about 4.2352941 hours, or 4 h 14 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/8 of the job and the second does 1/9.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 17/72 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 8 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{8} + \frac{1}{9} = \frac{1}{t}\ \Rightarrow\ t = \frac{72}{17} \]
\[ \frac{1}{8} + \frac{1}{9} = \frac{9 + 8}{72} = \frac{17}{72} \]
\[ t = \frac{72}{17} = \frac{72}{17} \approx 4.2352941\text{ hours} \]Questions
How long do they take together?
Working together they take 72/17 hours (about 4.2352941 hours, or 4 h 14 min).