SOLUTION: Team A can fix a car 6 hours faster than Team B. If two teams work together, they can fix a car in 4 hours. How long will it take each team, working separately, to fix a car?

Let t be the time for the slower team.

Then time for the faster team is (t-6).


The "combined rate" equation is

 +  = .


4*(t-6) + 4t = t*(t-6)

t^2 - 14t + 24 = 0

(t-12)*(t-2) = 0.

There are two roots,  t = 12  and t = 2.


But t-6 must be positive, and it leaves ONLY one root t= 12 hours for the slower team.


Then for the faster team time is  12-6 = 6 hours.


Check.   +  =  =  = .  ! Correct !.