## Elementary Algebra

Let t be the time it takes with the power mower. Thus: $1 = \frac{20}{t} + \frac{30}{t-40}$ We create common denominators to obtain: $1 = \frac{30t+20t-800}{t(t-40)} \\ 30t+20t-800 = t^2 - 40t \\ t^2 -90t + 800 = 0 \\ (t-80)(t-10)$ Since she already took 30 minutes, 10 minutes does not make sense. Thus, the answer is: 80 minutes.