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

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 !