One person does a job in 4 hours and another in 5 hours. How long together?
Working together they take 20/9 hours (about 2.2222222 hours, or 2 h 13 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/4 of the job and the second does 1/5.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 9/20 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 4 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{4} + \frac{1}{5} = \frac{1}{t}\ \Rightarrow\ t = \frac{20}{9} \]
\[ \frac{1}{4} + \frac{1}{5} = \frac{5 + 4}{20} = \frac{9}{20} \]
\[ t = \frac{20}{9} = \frac{20}{9} \approx 2.2222222\text{ hours} \]Questions
How long do they take together?
Working together they take 20/9 hours (about 2.2222222 hours, or 2 h 13 min).