The rate a computer works is 1/time. Working together, you add the rates.
Let new computer be x, old computer be y.
x = y - 7
[tex]\frac{1}{x} + \frac{1}{y} = \frac{1}{13} \\ \\ \frac{1}{y-7}+\frac{1}{y} = \frac{1}{13} \\ \\ \frac{2y-7}{y(y-7)} = \frac{1}{13} \\ \\ y(y-7) = 13(2y-7) \\ \\ y^2-33y+91 = 0 \\ \\ y = 29.96 \\ \\ x = y-7 = 29.96-7 = 22.96[/tex]
Rounded to nearest tenth gives:
x = 23 hours
