Math / Numbers & Operations

QuestionA cyclist rides his bike at a speed of 18 miles per hour. What is this speed in feet per second? How many feet will the cyclist travel in 5 seconds? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers.

Studdy Solution

STEP 1

1. The cyclist's speed is given as $18$ miles per hour.
2. We need to convert this speed into feet per second.
3. Use the conversion $1 \text{ mile} = 5280 \text{ feet}$ .
4. We need to calculate the distance traveled in $5$ seconds.

STEP 2

1. Convert miles per hour to feet per hour.
2. Convert feet per hour to feet per second.
3. Calculate the distance traveled in 5 seconds.

STEP 3

Convert the speed from miles per hour to feet per hour using the conversion factor $1 \text{ mile} = 5280 \text{ feet}$ .
$18 \text{ miles per hour} \times 5280 \text{ feet per mile} = 95040 \text{ feet per hour}$

STEP 4

Convert feet per hour to feet per second by dividing by the number of seconds in an hour ( $3600$ seconds).
$\frac{95040 \text{ feet per hour}}{3600 \text{ seconds per hour}} = 26.4 \text{ feet per second}$

STEP 5

Calculate the distance traveled in 5 seconds by multiplying the speed in feet per second by the time in seconds.
$26.4 \text{ feet per second} \times 5 \text{ seconds} = 132 \text{ feet}$
The cyclist's speed in feet per second is:
$\boxed{26.4 \text{ feet per second}}$
The distance traveled in 5 seconds is:
$\boxed{132 \text{ feet}}$

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