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Sagot :
To solve the problem of determining Morris's speed given that he travels 3 feet per second less than Aneesha, let's work through the conversion and calculations step-by-step.
Step 1: Convert Aneesha's speed from miles per hour to feet per second.
Aneesha's speed is [tex]\( 50 \)[/tex] miles per hour. We need to convert this speed to feet per second.
[tex]\[ 1 \text{ mile} = 5,280 \text{ feet} \][/tex]
[tex]\[ 1 \text{ hour} = 3,600 \text{ seconds} \][/tex]
So, to convert miles per hour to feet per second, we use the formula:
[tex]\[ \text{speed in feet per second} = \text{speed in miles per hour} \times \frac{\text{feet per mile}}{\text{seconds per hour}} \][/tex]
Plugging in the values:
[tex]\[ \text{Aneesha's speed in feet per second} = 50 \text{ miles per hour} \times \frac{5,280 \text{ feet}}{3,600 \text{ seconds}} \][/tex]
Calculating this:
[tex]\[ \text{Aneesha's speed in feet per second} \approx 73.333 \text{ feet per second} \][/tex]
Step 2: Determine Morris's speed in feet per second.
Morris is traveling 3 feet per second less than Aneesha. So, we subtract 3 feet per second from Aneesha's speed:
[tex]\[ \text{Morris's speed in feet per second} = 73.333 \text{ feet per second} - 3 \text{ feet per second} \][/tex]
[tex]\[ \text{Morris's speed in feet per second} \approx 70.333 \text{ feet per second} \][/tex]
Step 3: Convert Morris's speed from feet per second back to miles per hour.
Again, we use the conversion factors:
[tex]\[ 1 \text{ mile} = 5,280 \text{ feet} \][/tex]
[tex]\[ 1 \text{ hour} = 3,600 \text{ seconds} \][/tex]
To convert feet per second to miles per hour, we use:
[tex]\[ \text{speed in miles per hour} = \text{speed in feet per second} \times \frac{3,600 \text{ seconds}}{5,280 \text{ feet}} \][/tex]
Plugging in Morris's speed:
[tex]\[ \text{Morris's speed in miles per hour} = 70.333 \text{ feet per second} \times \frac{3,600 \text{ seconds}}{5,280 \text{ feet}} \][/tex]
Calculating this:
[tex]\[ \text{Morris's speed in miles per hour} \approx 47.955 \text{ miles per hour} \][/tex]
Therefore, the most accurate rate of speed Morris is traveling is approximately [tex]\( 47.955 \)[/tex] miles per hour.
When rounding to the nearest whole number, Morris's speed is approximately [tex]\( 48 \)[/tex] miles per hour.
Thus, the most accurate rate of speed Morris is traveling is indeed 48 miles per hour.
Step 1: Convert Aneesha's speed from miles per hour to feet per second.
Aneesha's speed is [tex]\( 50 \)[/tex] miles per hour. We need to convert this speed to feet per second.
[tex]\[ 1 \text{ mile} = 5,280 \text{ feet} \][/tex]
[tex]\[ 1 \text{ hour} = 3,600 \text{ seconds} \][/tex]
So, to convert miles per hour to feet per second, we use the formula:
[tex]\[ \text{speed in feet per second} = \text{speed in miles per hour} \times \frac{\text{feet per mile}}{\text{seconds per hour}} \][/tex]
Plugging in the values:
[tex]\[ \text{Aneesha's speed in feet per second} = 50 \text{ miles per hour} \times \frac{5,280 \text{ feet}}{3,600 \text{ seconds}} \][/tex]
Calculating this:
[tex]\[ \text{Aneesha's speed in feet per second} \approx 73.333 \text{ feet per second} \][/tex]
Step 2: Determine Morris's speed in feet per second.
Morris is traveling 3 feet per second less than Aneesha. So, we subtract 3 feet per second from Aneesha's speed:
[tex]\[ \text{Morris's speed in feet per second} = 73.333 \text{ feet per second} - 3 \text{ feet per second} \][/tex]
[tex]\[ \text{Morris's speed in feet per second} \approx 70.333 \text{ feet per second} \][/tex]
Step 3: Convert Morris's speed from feet per second back to miles per hour.
Again, we use the conversion factors:
[tex]\[ 1 \text{ mile} = 5,280 \text{ feet} \][/tex]
[tex]\[ 1 \text{ hour} = 3,600 \text{ seconds} \][/tex]
To convert feet per second to miles per hour, we use:
[tex]\[ \text{speed in miles per hour} = \text{speed in feet per second} \times \frac{3,600 \text{ seconds}}{5,280 \text{ feet}} \][/tex]
Plugging in Morris's speed:
[tex]\[ \text{Morris's speed in miles per hour} = 70.333 \text{ feet per second} \times \frac{3,600 \text{ seconds}}{5,280 \text{ feet}} \][/tex]
Calculating this:
[tex]\[ \text{Morris's speed in miles per hour} \approx 47.955 \text{ miles per hour} \][/tex]
Therefore, the most accurate rate of speed Morris is traveling is approximately [tex]\( 47.955 \)[/tex] miles per hour.
When rounding to the nearest whole number, Morris's speed is approximately [tex]\( 48 \)[/tex] miles per hour.
Thus, the most accurate rate of speed Morris is traveling is indeed 48 miles per hour.
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