One person does a job in 4 hours and another in 12 hours. How long together?
Working together they take 3 hours.
How to work it out
- 1
Think in rates: in one hour the first does 1/4 of the job and the second does 1/12.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 16/48 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
\[ \frac{1}{4} + \frac{1}{12} = \frac{1}{t}\ \Rightarrow\ t = 3 \]
\[ \frac{1}{4} + \frac{1}{12} = \frac{12 + 4}{48} = \frac{16}{48} \]
\[ t = \frac{48}{16} = 3 \approx 3\text{ hours} \]Questions
How long do they take together?
Working together they take 3 hours.