One person does a job in 9 hours and another in 10 hours. How long together?
Working together they take 90/19 hours (about 4.7368421 hours, or 4 h 44 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/9 of the job and the second does 1/10.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 19/90 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 9 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{9} + \frac{1}{10} = \frac{1}{t}\ \Rightarrow\ t = \frac{90}{19} \]
\[ \frac{1}{9} + \frac{1}{10} = \frac{10 + 9}{90} = \frac{19}{90} \]
\[ t = \frac{90}{19} = \frac{90}{19} \approx 4.7368421\text{ hours} \]Questions
How long do they take together?
Working together they take 90/19 hours (about 4.7368421 hours, or 4 h 44 min).