Shelly can cut the lawn

Question

Shelley can cut a lawn with the riding mower in three hours less time than it takes William to cut the lawn with the push mower. If they can cut the lawn in three hours working together find her along to the nearest 10th of an hour it takes for William to cut the lawn alone.

Answer 1

Let x = time it takes William to cut the lawn by himself

Then, x-3 = time it takes Shelley to cut the lawn alone

1/x = portion of the lawn cut by William in 1 hour

1/(x-3) = portion of the lawn cut by Shelley in 1 hour

1/3 = portion of the lawn cut by both mowers in 1 hour

So, 1/x + 1/(x-3) = 1/3

3(x-3) + 3x = x(x-3)

x² - 9x + 9 = 0

x = [9 ± √45] / 2 = 7.9 or 1.1

If x = 1.1, then x-3 < 0. So, the only solution is x = 7.9.

William, when working alone, cuts the lawn in 7.9 hours.