Question

A new computer can complete a complex biochemistry calculation in 7 hours less than an older-model computer. Working together, the new computer and the old computer can complete the calculation in 13 hours. How long would it take the new computer to complete the calculation by itself? Round to the nearest tenth of an hour.

Answer 1

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

$\frac{1}{x} + \frac{1}{y} = \frac{1}{13} \\ \\ \frac{1}{y-7}+\frac{1}{y} = \frac{1}{13} \\ \\ \frac{2y-7}{y(y-7)} = \frac{1}{13} \\ \\ y(y-7) = 13(2y-7) \\ \\ y^2-33y+91 = 0 \\ \\ y = 29.96 \\ \\ x = y-7 = 29.96-7 = 22.96$
Rounded to nearest tenth gives:
x = 23 hours