To determine the rate as a fraction in simplest form for the given scenario, let's break down the steps involved.
1. Understand the Units and Values:
- We need to express a rate of 280 miles in [tex]\(10 \frac{1}{2}\)[/tex] hours.
2. Convert Mixed Number to Decimal:
- Convert [tex]\(10 \frac{1}{2}\)[/tex] hours into decimal form.
- [tex]\(10 \frac{1}{2} = 10 + 0.5 = 10.5\)[/tex] hours.
3. Calculate the Rate:
- Divide the total distance (280 miles) by the total time (10.5 hours) to determine the rate.
- The rate would be [tex]\( \frac{280}{10.5} \)[/tex] miles per hour.
4. Simplify the Fraction:
- Simplify this rate by finding the greatest common divisor (GCD) of the numerator and the denominator. Based on the process, the simplest form of the fraction [tex]\( \frac{280}{10.5} \)[/tex] becomes [tex]\( \frac{28}{1.0} \)[/tex].
5. Result:
- The calculation results in 28 miles per hour after simplification.
Now, choosing the correct option:
- Option A: The fraction should be in miles per hour.
- The simplified rate in fraction form is: [tex]\( \frac{28 \text{ miles}}{1.0 \text{ hour}} \)[/tex].
Therefore, the full answer is, assuming the best choice in context:
A. The rate written as a fraction in simplest form is [tex]\( 28 \)[/tex] miles [tex]\( 1.0 \)[/tex] hour
