Let x be the time (in minutes) it takes using the power mower, let y be the time (in minutes) it takes using the hand mower.

y = x + 20 .... (1)

After 15 minutes the fraction of time remaining to do the line and hence the fraction of lawn still to be mowed is

. So the time it will take to finish the job using the hand mower is

.

But taking 25 minutes more to complete the job means that the lawn got mowed in 15 + 25 = 40 minutes. Hence:

[tex]15 + \frac{x - 15}{x} \cdot y = 40 \Rightarrow 15x + (x - 15)y = 40x

.... (2)

Substitute equation (1) into equation (2):

.

You want the positive solution to this equation. I get x = 30.