To determine the most accurate rate of speed Morris is traveling, let's work through the problem step-by-step.
1. Convert Aneesha's speed from miles per hour to feet per second:
- Aneesha travels at a rate of 50 miles per hour.
- 1 mile = 5280 feet.
- 1 hour = 3600 seconds.
Therefore, Aneesha's speed in feet per second can be calculated as:
[tex]\[
\text{Speed of Aneesha in fps} = 50 \, \text{miles/hour} \times \frac{5280 \, \text{feet}}{1 \, \text{mile}} \times \frac{1 \, \text{hour}}{3600 \, \text{seconds}}
\][/tex]
This simplifies to:
[tex]\[
\text{Speed of Aneesha in fps} = 50 \times \frac{5280}{3600} = 73.3333 \, \text{feet/second}
\][/tex]
2. Calculate Morris's speed in feet per second:
- Morris is traveling 3 feet per second less than Aneesha.
- Therefore, Morris's speed in feet per second is:
[tex]\[
\text{Speed of Morris in fps} = 73.3333 - 3 = 70.3333 \, \text{feet/second}
\][/tex]
3. Convert Morris's speed from feet per second back to miles per hour:
- 1 mile = 5280 feet.
- 1 hour = 3600 seconds.
Therefore, Morris's speed in miles per hour can be calculated as:
[tex]\[
\text{Speed of Morris in mph} = 70.3333 \, \text{feet/second} \times \frac{3600 \, \text{seconds}}{1 \, \text{hour}} \times \frac{1 \, \text{mile}}{5280 \, \text{feet}}
\][/tex]
This simplifies to:
[tex]\[
\text{Speed of Morris in mph} = 70.3333 \times \frac{3600}{5280} = 47.9545 \, \text{miles/hour}
\][/tex]
Therefore, the most accurate rate of speed Morris is traveling is approximately 47.95 miles per hour.
Conclusion:
Among the given options [tex]\(45\)[/tex] miles per hour, [tex]\(46\)[/tex] miles per hour, [tex]\(47\)[/tex] miles per hour, and [tex]\(48\)[/tex] miles per hour, the closest rate of speed to 47.95 miles per hour is:
47 miles per hour
So the most accurate rate of speed Morris is traveling is [tex]\(\boxed{47 \, \text{miles/hour}}\)[/tex].
