One person does a job in 4 hours and another in 10 hours. How long together?
Working together they take 20/7 hours (about 2.8571429 hours, or 2 h 51 min).
How to work it out
- 1
Think in rates: in one hour the first does 1/4 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 14/40 of the job per hour, the whole job takes the reciprocal:
- 4
Check: that is less than 4 hours, the faster worker alone, as it should be ✓
LaTeX source of the formulas on this page
\[ \frac{1}{4} + \frac{1}{10} = \frac{1}{t}\ \Rightarrow\ t = \frac{20}{7} \]
\[ \frac{1}{4} + \frac{1}{10} = \frac{10 + 4}{40} = \frac{14}{40} \]
\[ t = \frac{40}{14} = \frac{20}{7} \approx 2.8571429\text{ hours} \]Questions
How long do they take together?
Working together they take 20/7 hours (about 2.8571429 hours, or 2 h 51 min).