One person does a job in 5 hours and another in 9 hours. How long together?
Working together they take 45/14 hours (about 3.2142857 hours, or 3 h 13 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 1/9.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 14/45 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
\[ \frac{1}{5} + \frac{1}{9} = \frac{1}{t}\ \Rightarrow\ t = \frac{45}{14} \]
\[ \frac{1}{5} + \frac{1}{9} = \frac{9 + 5}{45} = \frac{14}{45} \]
\[ t = \frac{45}{14} = \frac{45}{14} \approx 3.2142857\text{ hours} \]Questions
How long do they take together?
Working together they take 45/14 hours (about 3.2142857 hours, or 3 h 13 min).