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.

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