Two young boys, Bob and Tom, are mowing grass one summer as a means of making money to save for their college education. They always split the work and proceeds equally. They have one lawnmower. They obtain a new job which involves mowing a 40' by 80' rectangular vacant lot. The owner wants it mowed in a collapsing pattern (begin mowing around the outside perimeter, with each pass moving closer to the center of the lot). Bob will mow first, turning the work over to Tom when he has mowed exactly half the area. Bob decides that he will stop at a uniform distance in from the perimeter on all sides, leaving a remaining rectangle for Tom to complete. At what uniform distance (in feet to 2 decimal places) should Bob stop mowing?

Make a sketch of a rectangle and another similar rectangle inside.

The dimensions of the outer rectangle is 80' by 40' for an area of 3200'. Now the area of the smaller rectangle will be 1600'.

Let the shorter side be x. The longer side will be 2x, since the longer side is twice the length of the shorter one.

Then, you know that the product of this two sides give the area of the smaller rectangle, that is:

2x \times x = 1600

2x^2 = 1600

Solve for x.

From this, you can deduce how far from the perimeter Bob should stop.