Question

Julio walks 264 feet per minute. What is his rate in miles per hour? (Hint: 1 mile = 5280 feet.) A. 3 miles per hour B. 3.5 miles per hour C. 4 miles per hour D. 4.5 miles per hour

Short answer

3 miles per hour (A).

Step-by-step solution

Understand the Question

Julio's walking rate needs to be converted from feet per minute to miles per hour. This involves converting both the distance (feet to miles) and the time (minutes to hours) appropriately.

Convert Feet to Miles

There are 5280 feet in a mile. To find out how many miles he walks per minute, divide the number of feet Julio walks per minute by the number of feet in a mile:time = \(\frac{264}{5280}\)

Calculate the Conversion

Perform the division to convert feet to miles:\(\frac{264 \text{ feet}}{5280 \text{ feet per mile}} = 0.05 \text{ miles per minute}\)

Convert Minutes to Hours

Since there are 60 minutes in an hour, multiply the result by 60 to convert minutes to hours:\(0.05 \text{ miles per minute} \times 60 \text{ minutes per hour} = 3 \text{ miles per hour}\)

Identify the Correct Answer

The correct answer is 3 miles per hour, corresponding to option A.

Key concepts

Unit Conversion

In many problems, you need to convert units to make calculations easier. Unit conversion is the process of switching between different units of measure. In this exercise, we converted feet per minute to miles per hour.
Julio walks 264 feet per minute, but we want this rate in miles per hour. We need to change feet to miles and minutes to hours.
This requires knowing the conversion factors: 1 mile = 5280 feet and 1 hour = 60 minutes.
These two conversions help simplify the whole calculation process.

Rate Calculation

Rate calculation involves finding how much of something happens over a particular time. Here, it's how many miles Julio walks per hour.
The rate in the problem starts in feet per minute. To properly convert, divide the feet walked per minute by the number of feet in a mile:
\[\frac{264 \text{ feet}}{5280 \text{ feet per mile}}\]
The result is the rate in miles per minute. Multiplying this by the number of minutes in an hour gives us the rate in miles per hour:
\[0.05 \text{ miles per minute} \times 60 \text{ minutes per hour} = 3 \text{ miles per hour}\]
This shows how much distance Julio covers in a longer time.

Distance and Time Conversion

Converting between different units of distance and time is crucial for solving rate problems. Here, we went from smaller units (feet and minutes) to larger units (miles and hours).
First, convert the smaller distance unit (feet) to the larger unit (miles):
\[\frac{264 \text{ feet}}{5280 \text{ feet per mile}}\]The result, 0.05, tells us how many miles Julio walks in one minute.
Next, convert this minute-based rate to an hour-based rate by multiplying by 60 (since there are 60 minutes in an hour):
\[0.05 \text{ miles per minute} \times 60 \text{ minutes per hour} = 3 \text{ miles per hour}\]
By understanding and applying these conversions, we can easily find the correct rate.