One person does a job in 7 hours and another in 9 hours. How long together?
Working together they take 63/16 hours (about 3.9375 hours, or 3 h 56 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 1/9.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 16/63 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
\[ \frac{1}{7} + \frac{1}{9} = \frac{1}{t}\ \Rightarrow\ t = \frac{63}{16} \]
\[ \frac{1}{7} + \frac{1}{9} = \frac{9 + 7}{63} = \frac{16}{63} \]
\[ t = \frac{63}{16} = \frac{63}{16} \approx 3.9375\text{ hours} \]Questions
How long do they take together?
Working together they take 63/16 hours (about 3.9375 hours, or 3 h 56 min).