Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the most accurate rate of speed Morris is traveling?

1 mile = 5,280 feet

A. 45 miles per hour
B. 46 miles per hour
C. 47 miles per hour
D. 48 miles per hour



Answer :

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].