One person does a job in 3 hours and another in 9 hours. How long together?
Working together they take 9/4 hours (about 2.25 hours, or 2 h 15 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 1/9.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 12/27 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
\[ \frac{1}{3} + \frac{1}{9} = \frac{1}{t}\ \Rightarrow\ t = \frac{9}{4} \]
\[ \frac{1}{3} + \frac{1}{9} = \frac{9 + 3}{27} = \frac{12}{27} \]
\[ t = \frac{27}{12} = \frac{9}{4} \approx 2.25\text{ hours} \]Questions
How long do they take together?
Working together they take 9/4 hours (about 2.25 hours, or 2 h 15 min).