Question

Moe uses a mower to cut his rectangular (x)-foot by (y)-foot lawn. The swath he cuts is (z) inches wide, but he overlaps each cut by (w) inches to make sure that no grass is missed. He walks at the rate of (r) feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow the lawn?

a) ( xywrz )
b) ( x + yr + z )
c) ( xyzr + wz )
d) ( x + y + z + wr )

Answer 1

The expression xy / r represents the closest estimation of the number of hours it will take Moe to mow the lawn.

None of the given options is correct

Step-by-step explanation:

To find the number of hours it will take Moe to mow the lawn, we need to consider the area he needs to cover and his walking speed.

The area of the rectangular lawn is given by the formula A = x * y, where x represents the length of the lawn in feet and y represents the width of the lawn in feet.

The width of the swath Moe cuts is z inches, which is equivalent to z/12 feet. However, since Moe overlaps each cut by w inches, we need to subtract w/12 from the width of the swath. So the effective width of each cut is (z - w)/12 feet.

To calculate the number of cuts needed to cover the lawn, we divide the width of the lawn by the effective width of each cut: y / [(z - w)/12].

Since Moe walks at a rate of r feet per hour, the time it takes him to mow one cut is [(z - w)/12] / r.

Therefore, the total time it will take Moe to mow the entire lawn is given by the formula:

[(x * y) / (y / [(z - w)/12])] * [(z - w)/12] / r

Simplifying this expression gives us:

(xy * 12) / (z - w) * (z - w) / (12r)

The (z - w) terms cancel out, leaving us with:

xy / r

None of the given options is correct