One person does a job in 4 hours and another in 8 hours. How long together?
Working together they take 8/3 hours (about 2.6666667 hours, or 2 h 40 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 1/8.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 12/32 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
\[ \frac{1}{4} + \frac{1}{8} = \frac{1}{t}\ \Rightarrow\ t = \frac{8}{3} \]
\[ \frac{1}{4} + \frac{1}{8} = \frac{8 + 4}{32} = \frac{12}{32} \]
\[ t = \frac{32}{12} = \frac{8}{3} \approx 2.6666667\text{ hours} \]Questions
How long do they take together?
Working together they take 8/3 hours (about 2.6666667 hours, or 2 h 40 min).