Moe uses a mower to cut his rectangular -foot by -foot lawn. The swath he cuts is inches wide, but he overlaps each cut by inches to make sure that no grass is missed. He walks at the rate of 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)
- B)
- C)
- D)
- E)
Answer
C
Key insight
The overlap makes each pass effectively 24 inches = 2 feet wide, so Moe clears 5000 times 2 = 10000 square feet per hour against a 13500 square foot lawn.
Solution
Because each pass overlaps the previous one by inches, every pass adds only inches of new grass, which is exactly feet.
While walking feet in an hour, Moe therefore clears a strip feet long and feet wide: square feet per hour.
The lawn has area square feet, so the time needed is
The answer is .
Why this works
A mowing rate is "area per hour," and area per hour is walking speed times effective width. The overlap is a distraction only until you realize it just shrinks the useful width to feet. Convert units first, then compute; the direction of the lawn (mowing along the -foot or the -foot side) does not matter because the total distance walked equals total area divided by strip width.
Alternative approach
Mow parallel to the -foot side: each strip is feet, and strips are needed, giving feet of walking, or hours.
The trap
Using the full 28-inch swath (or adding the 4 inches instead of subtracting) and forgetting to convert inches to feet.
Common mistakes
- Using the full -inch swath (or adding the inches instead of subtracting) and forgetting to convert inches to feet.
- Dividing by (ignoring the swath width entirely) to get , then choosing the nearest option .
Techniques
Set up the equation/formula and compute; no special trick needed