One person does a job in 5 hours and another in 7 hours. How long together?
Working together they take 35/12 hours (about 2.9166667 hours, or 2 h 55 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/5 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 12/35 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 5 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{5} + \frac{1}{7} = \frac{1}{t}\ \Rightarrow\ t = \frac{35}{12} \]
\[ \frac{1}{5} + \frac{1}{7} = \frac{7 + 5}{35} = \frac{12}{35} \]
\[ t = \frac{35}{12} = \frac{35}{12} \approx 2.9166667\text{ hours} \]Questions
How long do they take together?
Working together they take 35/12 hours (about 2.9166667 hours, or 2 h 55 min).