Question

Parallel processing that uses two or more computers working together to solve a single problem using parallel processing two computers can solve a problem in 20 minutes so that's a together amount together is 20 minutes if working alone one computer can solve a problem in nine minutes less than the time needed by the second computer. How long will it take the faster computer working alone to solve the problem?

Answer 1

Let x = amount of time, in min, the slower computer can do the task (on its own)

We can write:

`(1)/(x-9)+(1)/(x)=(1)/(20)`

Note: we equated the rates of both. Time and rates are reciprocal of each other.

Let's solve this equation:

`\begin{gathered} (1)/(x-9)+(1)/(x)=(1)/(20) \\ (1(x)+1(x-9))/(x(x-9))=(1)/(20) \\ (x+x-9)/(x^2-9x)=(1)/(20) \\ (2x-9)/(x^2-9x)=(1)/(20) \\ 1(x^2-9x)=20(2x-9) \\ x^2-9x=40x-180 \\ x^2-49x+180=0 \\ (x-45)(x-4)=0 \\ x=4,45 \end{gathered}`

Recall,

x is time of slower computer

x - 9 is time of faster computer

If we take x = 4, "x - 9" becomes negative. So, this solution wouldn't be possible. We take x = 45 as our answer.

So,

faster computer time = x - 9 = 45 - 9 = 36 minutes