One person does a job in 3 hours and another in 5 hours. How long together?
Working together they take 15/8 hours (about 1.875 hours, or 1 h 53 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/3 of the job and the second does 1/5.
- 2
Together in one hour they do the sum of the rates:
- 3
If they do 8/15 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 3 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{3} + \frac{1}{5} = \frac{1}{t}\ \Rightarrow\ t = \frac{15}{8} \]
\[ \frac{1}{3} + \frac{1}{5} = \frac{5 + 3}{15} = \frac{8}{15} \]
\[ t = \frac{15}{8} = \frac{15}{8} \approx 1.875\text{ hours} \]Questions
How long do they take together?
Working together they take 15/8 hours (about 1.875 hours, or 1 h 53 min).