To determine Morris's speed in miles per hour, let's go through a step-by-step solution:
1. Convert Aneesha's speed from miles per hour to feet per second:
- Aneesha's speed is 50 miles per hour.
- There are 5280 feet in one mile.
- There are 3600 seconds in one hour.
First, convert Aneesha's speed from miles per hour to feet per second:
[tex]\[
\text{Aneesha's speed (feet/second)} = \left( 50 \, \text{miles/hour} \right) \times \left( \frac{5280 \, \text{feet}}{1 \, \text{mile}} \right) \times \left( \frac{1 \, \text{hour}}{3600 \, \text{seconds}} \right)
\][/tex]
Simplifying, we get:
[tex]\[
\text{Aneesha's speed (feet/second)} = \left( 50 \times 5280 \right) / 3600 = 73.33 \, \text{feet/second}
\][/tex]
2. Calculate Morris's speed in feet per second:
- Morris is traveling 3 feet per second less than Aneesha.
- Aneesha's speed is 73.33 feet per second.
Therefore, Morris's speed in feet per second:
[tex]\[
\text{Morris's speed (feet/second)} = 73.33 \, \text{feet/second} - 3 \, \text{feet/second} = 70.33 \, \text{feet/second}
\][/tex]
3. Convert Morris's speed from feet per second back to miles per hour:
- We need to convert feet per second to miles per hour. We use the same conversion factors in reverse:
- There are 5280 feet in one mile.
- There are 3600 seconds in one hour.
Therefore, Morris's speed in miles per hour:
[tex]\[
\text{Morris's speed (miles/hour)} = \left( 70.33 \, \text{feet/second} \right) \times \left( \frac{3600 \, \text{seconds}}{1 \, \text{hour}} \right) \times \left( \frac{1 \, \text{mile}}{5280 \, \text{feet}} \right)
\][/tex]
Simplifying, we get:
[tex]\[
\text{Morris's speed (miles/hour)} = \left( 70.33 \times 3600 \right) / 5280 = 48 \, \text{miles/hour}
\][/tex]
Thus, Morris is traveling at a speed of 48 miles per hour. So, the most accurate rate of speed Morris is traveling is 48 miles per hour.
