One person does a job in 6 hours and another in 7 hours. How long together?
Working together they take 42/13 hours (about 3.2307692 hours, or 3 h 14 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/6 of the job and the second does 1/7.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 13/42 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 6 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{6} + \frac{1}{7} = \frac{1}{t}\ \Rightarrow\ t = \frac{42}{13} \]
\[ \frac{1}{6} + \frac{1}{7} = \frac{7 + 6}{42} = \frac{13}{42} \]
\[ t = \frac{42}{13} = \frac{42}{13} \approx 3.2307692\text{ hours} \]Questions
How long do they take together?
Working together they take 42/13 hours (about 3.2307692 hours, or 3 h 14 min).