Joe can wax the gym floor in 3 hours. Steve can wax it in 2 hours. How long will the job take if they work together?

Answer 1

Koli, 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,

Tj = 3 (time for Joe to do the job)

Ts = 2 (time for Steve to do the job)

and the Rates are their reciprocals

R_j = 1/T_j

R_s = 1/T_s

For combined work

1 = T (Rj + Rs)

Where Rj = 1/Tj and Rs = 1/Ts

1 = T (1/3 + 1/2)

1 = T (5/6)

T = 6/5 hour