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?

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Question 1111318: 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?

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!
Team A
Team B
A & B


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.
.






Team A, fix one car alone, 6 hours
Team B, fix one car alone, 12 hours


-
check



,
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
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 !.

Solved.

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It is a typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive
    - Using quadratic equations to solve word problems on joint work (*)

Read them and get be trained in solving joint-work problems.
Pay special attention to the lesson marked (*) in the list.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



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