One person does a job in 10 hours and another in 10 hours. How long together?
Working together they take 5 hours.
How to work it out
- 1
Think in rates: in one hour the first does 1/10 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 20/100 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 10 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{10} + \frac{1}{10} = \frac{1}{t}\ \Rightarrow\ t = 5 \]
\[ \frac{1}{10} + \frac{1}{10} = \frac{10 + 10}{100} = \frac{20}{100} \]
\[ t = \frac{100}{20} = 5 \approx 5\text{ hours} \]Questions
How long do they take together?
Working together they take 5 hours.