Question

When two computers are working together, they can finish updating software in 9 minutes. How long would they take individually to update the software if one computer takes 24 minutes longer than the other?

Answer 1

First computer takes x min. For 1 min it does 1/x part of work.

Second computer takes (x+24) min. For one min it does 1/(x+24) part of work.

Both computers for one min do   (1/x+1/(x+24)) part of work.

At the same time, both computers for one min do 1/9 part of work.

$\frac{1}{x} + \frac{1}{x+24} = \frac{1}{9} \\ \\ \frac{x+24+x}{x(x+24)} = \frac{1}{9} \\ \\9(2x+24)=x^{2} +24x \\ \\ 18x+216=x^{2} +24x \\ \\ x^{2}+6x-216=0 \\ \\ D=b^{2}-4ac=36+4*216 = 900 \\ \\ x= \frac{-b+/- \sqrt{D} }{2a} = \frac{-6+/-30}{2} \\ \\ x_{1}=-18, x_{2}=12 We can use only positive number here. So, for the first computer x=12 min, for second computer x+24=12+24= 36 min Answer 12 min and 36 min.$

Answer 2

It would take the computers 12 minutes and 36 minutes respectively to individually update the software

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let t represent the time it takes the fastest computer. Hence:

$(\frac{1}{t}+\frac{1}{t+24})9=1\\ \\ t=12 \ minutes$

It would take the computers 12 minutes and 36 minutes (12 + 24) respectively to individually update the software

Find out more on equation at: https://brainly.com/question/2972832