To solve this problem, we need to first understand the conversion between miles per hour (mph) and feet per second (fps). We'll break down the solution into clear and understandable steps.
1. Convert Aneesha's speed from miles per hour to feet per second.
Aneesha's speed is 50 miles per hour. We know that:
- 1 mile = 5,280 feet
- 1 hour = 3,600 seconds
Therefore, to convert miles per hour to feet per second, we use the formula:
[tex]\[
\text{Speed in feet per second} = \text{Speed in miles per hour} \times \frac{5280 \text{ feet}}{3600 \text{ seconds}}
\][/tex]
For Aneesha:
[tex]\[
\text{Speed in feet per second} = 50 \times \frac{5280}{3600}
\][/tex]
Upon simplification:
[tex]\[
\text{Speed in feet per second} = 50 \times 1.4667 \approx 73.3333 \text{ feet per second}
\][/tex]
2. Determine Morris's speed in feet per second.
Morris is traveling 3 feet per second less than Aneesha. So:
[tex]\[
\text{Speed in feet per second (Morris)} = 73.3333 - 3 = 70.3333 \text{ feet per second}
\][/tex]
3. Convert Morris's speed back to miles per hour.
Now, we need to convert feet per second back to miles per hour. We use the reverse of the initial conversion formula:
[tex]\[
\text{Speed in miles per hour} = \text{Speed in feet per second} \times \frac{3600 \text{ seconds}}{5280 \text{ feet}}
\][/tex]
For Morris:
[tex]\[
\text{Speed in miles per hour} = 70.3333 \times \frac{3600}{5280}
\][/tex]
Simplifying this:
[tex]\[
\text{Speed in miles per hour} = 70.3333 \times 0.6818 \approx 48 \text{ miles per hour}
\][/tex]
Therefore, the most accurate rate of speed Morris is traveling is:
48 miles per hour.
