Jeff probably is hard-working person and finish his job within $a$ hours and his friend Joe, ends the same job within $b$ hours. Now, if they work together job is done by $$\frac{ab}{a+b}$$ hours of working. Why ? I'll appreciate any illustration by proving the statement. Thank you!
2026-04-24 19:44:40.1777059880
Given the times needed by two workers to complete a task, how long will they need to do it together?
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1
In one hour $(a,b>0)$:
Jeff will complete $\dfrac{1}{a}$ of the work (there is ONE job).
Joe will complete $\dfrac{1}{b}$ of the work.
Jeff and Joe will complete $\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{a+b}{ab}$ of the work together.
So the time needed when two people work together to complete that ONE job is $1\div\dfrac{a+b}{ab}=\dfrac{ab}{a+b}$ hours.