One person does a job in 7 hours and another in 10 hours. How long together?
Working together they take 70/17 hours (about 4.1176471 hours, or 4 h 7 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/7 of the job and the second does 1/10.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 17/70 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 7 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{7} + \frac{1}{10} = \frac{1}{t}\ \Rightarrow\ t = \frac{70}{17} \]
\[ \frac{1}{7} + \frac{1}{10} = \frac{10 + 7}{70} = \frac{17}{70} \]
\[ t = \frac{70}{17} = \frac{70}{17} \approx 4.1176471\text{ hours} \]Questions
How long do they take together?
Working together they take 70/17 hours (about 4.1176471 hours, or 4 h 7 min).