Maria​, an experienced shipping​ clerk, can fill a certain order in 7 hours. Felipe​, a new​ clerk, needs 10 hours to do the same job. Working​ together, how long will it take them to fill the​ order?

Answer 1

Kelsey,  the key to “shared work” problems is to understand Work, Rate, and Time.

Work = Rate * Time

( w = r t )

Work is the amount of effort expended or material produced.

Rate is how fast someone can do the work ( what fraction of the work gets done in an hour. Or how many jobs per month, etc.)

Time is the amount of time it takes someone to get the job done.

If the amount of work is 1 job, then the rates and times are reciprocals:

1 = RT or R = 1/T or T = 1/R

in this problem, the Times are

Tm = 7

Tf = 10

Working together, you need to add Rates, so let’s name the rates as well

Rm = 1/Tm = 1/7

Rf = 1/Tf = 1/10

1 = T (Rm + Rf) = T(1/7 + 1/10)

Solve for T

1 = T(17/70)

T = 70/17 hours