Answer:
When they work together, they complete the sales routine in 2.1 hours
Step-by-step explanation:
We know the time needed to complete the job for each separately, but our unknown "x" is the time when they work together.
We analyse what is the portion of the job they complete in the unit of time (in this case: hour)
We say: "Because it takes Jane 3 hours to complete the routine, the part of the routine done by Jane in one hour would be": 1/3 (one third of the routine done in one hour).
We also understand that since it takes Dave 7 hours to complete the routine, then in one hour he would have completed 1/7 (one seventh) of the routine.
If they work together, and "x" is the amount of time they need to complete the routine, then, following the same reasoning, in one hour they would have completed 1/x of the routine.
We are ready to set our equation for the portion of the routine completed when they work together:
[tex]\frac{1}{x} =\frac{1}{3} +\frac{1}{7} \\\frac{1}{x} =\frac{7}{21} +\frac{3}{21}=\frac{10}{21}[/tex]
where we have written all fractions with the same denominator (finding their least common denominator) so we can add them.
Now we can solve for x (the number of hours to complete the job when they work together):
[tex]\frac{x}{1} =\frac{21}{10} =2.1[/tex] hours
We simply flipped both fractions to solved for "x"
