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Math  /  Algebra

QuestionCharlotte is driving at 71.5mi/h71.5 \mathrm{mi} / \mathrm{h} and receives a text message. She looks down at her phone and takes her eyes off the road for 3.92 s . How far has Charlotte traveled in feet during this time? distance: □\square ft

Studdy Solution

STEP 1

1. Charlotte's speed is constant during the time she is looking at her phone.
2. The speed given is in miles per hour (mi/h).
3. The time given is in seconds (s).
4. 1 mile is equivalent to 5280 feet.
5. We need to convert the speed from miles per hour to feet per second to find the distance traveled.

STEP 2

1. Convert the speed from miles per hour to feet per second.
2. Calculate the distance traveled in feet using the speed in feet per second and the time in seconds.

STEP 3

Convert the speed from miles per hour to feet per second.
First, recall the conversion factors: 1 mile=5280 feet 1 \text{ mile} = 5280 \text{ feet} 1 hour=3600 seconds 1 \text{ hour} = 3600 \text{ seconds}
The speed in feet per second is calculated as: 71.5 mi/h×5280 ft1 mi×1 h3600 s 71.5 \text{ mi/h} \times \frac{5280 \text{ ft}}{1 \text{ mi}} \times \frac{1 \text{ h}}{3600 \text{ s}}
Simplify the expression: 71.5×52803600 ft/s 71.5 \times \frac{5280}{3600} \text{ ft/s}

STEP 4

Calculate the numerical value of the speed in feet per second.
71.5×52803600=71.5×1.4667=104.857 ft/s 71.5 \times \frac{5280}{3600} = 71.5 \times 1.4667 = 104.857 \text{ ft/s}

STEP 5

Use the speed in feet per second to find the distance traveled in feet.
The distance traveled is given by: distance=speed×time \text{distance} = \text{speed} \times \text{time} distance=104.857 ft/s×3.92 s \text{distance} = 104.857 \text{ ft/s} \times 3.92 \text{ s}

STEP 6

Calculate the numerical value of the distance traveled.
distance=104.857×3.92=411.05144 ft \text{distance} = 104.857 \times 3.92 = 411.05144 \text{ ft}
Solution: Charlotte has traveled approximately 411.05 feet during the 3.92 seconds she took her eyes off the road.

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