Final answer:
To find the speed of the lawn mower, calculate the wheel circumference and convert it to miles, then multiply by the number of revolutions per minute and convert to hours, resulting in approximately 25/3 mph.
Step-by-step explanation:
The question aims to determine the speed of a lawn mower in miles per hour given that the wheels of the lawn mower have a 15-inch diameter and are rotating at 2.5 revolutions per minute.
First, we calculate the circumference of the wheels which is the distance they cover in one revolution. The formula for circumference is C = πd, where d is the diameter. Thus:
- C = π * 15 inches
- C = 3.14 * 15 inches
- C ≈ 47.1 inches
Next, we convert inches to miles knowing that 63360 inches is 1 mile:
- C ≈ 47.1 inches * (1 mile / 63360 inches)
- C ≈ 0.000743 miles
Then we find out how many miles the mower travels in a minute by multiplying the circumference by the number of revolutions per minute:
- ≈ 0.000743 miles/rev * 2.5 rev/min
- ≈ 0.001858 miles/min
To find the speed in miles per hour, we multiply the miles per minute by 60 (since there are 60 minutes in an hour):
- ≈ 0.001858 miles/min * 60 min/hr
- ≈ 0.11148 miles/hr
Finally, we simplify if needed to match one of the answer choices provided: