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