I need help solving this

Question

A new crew of painters can paint a small apartment in 12 hours. And experienced crew can paint the small apartment in six hours. How many hours does it take to paint the apartment when the two crews work together?

Answer 1

Chelsea, 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

Let Tn be the time taken by the new crew

Let Te be the time taken by the experienced crew.

Let Rn be the rate the new works at, = 1/ Tn

Let Re be the rate the experienced crew works at.

Re = 1/ Te

In this problem we are told

Tn = 12

Te = 6

and we want to answer

1 = T(Rn + Re) = T(1/Tn + 1/Te)

T = ?

Plug in the known values

1 = T (1/12 + 1/6)

Now solve for T