SOLUTION: One computer can solve a problem 5 minutes faster than a second computer. Working together, the computers can solve the problem in 6 minutes. How long does it take the faster compu

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Question 1138481: One computer can solve a problem 5 minutes faster than a second computer. Working together, the computers can solve the problem in 6 minutes. How long does it take the faster computer working alone to solve the problem?

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
x, time for the faster computer by itself.


Simplify and solve for x.

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Let x be the time for the faster computer to do the job working alone (in minutes).

Then the time for slower compute is (x+5) minutes, according to the condition.


Then their individual rates are   and  , giving the combined rate equal to the sum of individual rates.


It gives you an equation


     +  = 


To solve it, multiply both sides by 6x*(x+5). You will get


    6(x+5) + 6x =  x*(x+5)

    6x + 30 + 6x = x^2 + 5x

    x^2 - 7x - 30 = 0

    (x-10)*(x+3) = 0


The roots are 10 and -3, and only positive root is meaningful.


Answer.  The faster computer makes this job in 10 minutes, working alone.


CHECK.    +  =  +  =  =  = .   ! Correct !

Solved.

------------------

It is a standard and 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  (*)

Of this list,  the most relevant problems are in the lesson marked by  (*).
Read them and get be trained in solving joint-work problems.


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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