Question

Moe uses a mower to cut his rectangular $90$ -foot by $150$ -foot lawn. The swath he cuts is $28$ inches wide, but he overlaps each cut by $4$ inches to make sure that no grass is missed. He walks at the rate of $5000$ feet per hour while pushing the mower. Which of the following is closest to the number of hours it will take Moe to mow his lawn?

$0.75$

$0.8$

$1.35$

$1.5$

$3$

Answer: C

Concepts:rate area unit conversion

Difficulty rating: 1270

Small Hint:

Each pass effectively cuts a strip only $28 - 4 = 24$ inches wide because of the overlap

Big Hint:

A $24$ -inch strip is $2$ feet wide, so each foot walked mows $2$ square feet

Solution:

Because of the overlap, each pass adds a strip $28 - 4 = 24$ inches $= 2$ feet wide. So each foot Moe walks mows $2$ square feet, that is, $2 \cdot 5000 = 10000$ square feet per hour.

The lawn has area $90 \cdot 150 = 13500$ square feet, so the time is $\frac{13500}{10000} = 1.35$ hours.

Thus, the correct answer is C.

2003 AMC 12B Problem 4

Answer: C

Difficulty rating: 1270

Small Hint:

Big Hint:

Solution:

Problem 4 in Other Years