Question

Jim's favorite hockey player can shoot a hockey puck at a speed of 108 miles per hour. What is the speed of the puck in feet per second?
Hint: There are 5,280 feet in 1 mile.
Write your answer as a whole number, a decimal, or a simplified fraction or mixed number. Do not round.

Answer 1

To convert the speed from miles per hour to feet per second, we can use the conversions:

1. There are 5,280 feet in 1 mile.
2. There are 3,600 seconds in 1 hour.

Starting with the speed of 108 miles per hour, we can perform the conversion as follows:

\[
\text{Speed in feet per second} = 108 \text{ miles/hour} \times \frac{5280 \text{ feet/mile}}{3600 \text{ seconds/hour}}
\]

Now, let's compute this step-by-step:

1. Calculate the conversion factor:
\[
\frac{5280}{3600} = \frac{5280 \div 360}{3600 \div 360} = \frac{14.8}{10} = 1.48
\]
However, we will keep the original fraction for accuracy:
\[
\frac{5280}{3600} = \frac{528}{360} = \frac{44}{30} = \frac{22}{15}
\]

2. Now perform the multiplication:
\[
108 \times \frac{5280}{3600}
\]
This becomes:
\[
108 \times \frac{528}{360}
\]

3. Let's calculate it:
\[
108 \times \frac{44}{30} = \frac{108 \times 44}{30} = \frac{4752}{30}
\]

4. Now let's simplify \( \frac{4752}{30} \) if possible:
\[
\frac{4752 \div 6}{30 \div 6} = \frac{792}{5}
\]

Thus, the speed of the puck in feet per second is:
\[
\frac{792}{5} \text{ feet/second}
\]

If converted to a decimal, it is:
\[
792 \div 5 = 158.4 \text{ feet/second}
\]

So the final answer is:
\[
\frac{792}{5} \text{ feet/second} \quad \text{or} \quad 158.4 \text{ feet/second}
\]

Either can be acceptable based on the preferred format.