The Correct Answer and Explanation is:
Correct Answer: 1.1 miles per month
This problem requires converting a speed from feet per hour to miles per month using a method called dimensional analysis. This process involves multiplying the original value by a series of conversion factors, which are fractions equal to one, to systematically cancel out the old units and introduce the new ones.
The initial speed is 8 feet per hour. We can write this as a fraction: (8 feet / 1 hour).
First, we will convert the distance unit from feet to miles. According to the provided chart, 1 mile is equal to 5280 feet. To cancel out “feet” from the top of our fraction, we need a conversion factor with “feet” in the bottom. Therefore, we multiply by (1 mile / 5280 feet).
Next, we need to convert the time unit from hours to months. This is a two-step conversion. First, we convert hours to days. The chart states that 1 day equals 24 hours. To cancel “hours” from the bottom of our fraction, we multiply by a factor with “hours” on top: (24 hours / 1 day).
Then, we convert days to months. The chart provides the approximation that 1 month is about 30 days. To cancel “days” from the bottom of our new fraction, we multiply by a factor with “days” on top: (30 days / 1 month).
Now we can set up the complete equation:
(8 feet / 1 hour) × (1 mile / 5280 feet) × (24 hours / 1 day) × (30 days / 1 month)
Multiplying the numbers across the top and bottom gives us:
(8 × 1 × 24 × 30) miles / (1 × 5280 × 1 × 1) months = 5760 miles / 5280 months
Performing the division:
5760 ÷ 5280 ≈ 1.0909… miles per month
The final step is to round the answer to the nearest tenth. The tenths digit is 0, and the digit to its right is 9. Since 9 is 5 or greater, we round the tenths digit up to 1.
The final speed is 1.1 miles per month.
