Given the times needed by two workers to complete a task, how long will they need to do it together?

775 Views Asked by At

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!

1

There are 1 best solutions below

5
On BEST ANSWER

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.