Problem 1 - Prealgebra

Question

Express each of the following rates as a ratio with the given units. Miles/Hour A car travels 220 miles in 4 hours. What is the rate of the car in miles per hour? (IMAGE CANNOT COPY)

Step-by-Step Solution

Answer

The car travels at 55 miles per hour.

Step 1: Understand the Problem

A car travels 220 miles in 4 hours. We need to find the rate, which is the distance traveled in one hour, often referred to as miles per hour (mph).

Step 2: Set Up the Ratio

The problem describes a rate as 220 miles per 4 hours. This rate can be expressed as a ratio of the distance to time, or \( \frac{220\text{ miles}}{4\text{ hours}} \).

Step 3: Simplify the Ratio

To find the rate in miles per hour, divide 220 by 4. This provides the number of miles the car travels in each individual hour. Calculate \( \frac{220}{4} = 55 \).

Step 4: Conclude with the Unit

The rate of the car is 55 miles per hour, or 55 mph. This means that for every hour, the car travels 55 miles.

Key Concepts

Rate Calculation

Calculating rates, such as speed, is a practical skill often needed in everyday scenarios like traveling. Rates describe how one quantity changes relative to another. In essence, it's a ratio comparison. For instance, when figuring out speed, you're comparing distance to time.
To find a rate, you use a straightforward formula:

• Rate = \( \frac{\text{Distance}}{\text{Time}} \)

The above formula helps to determine how much distance is covered over a specific period.
For the exercise where a car travels 220 miles in 4 hours, we apply this principle. Set up the ratio of 220 miles divided by 4 hours. Simplifying this gives the car's rate as 55 miles per hour.

Miles Per Hour

"Miles per hour" (mph) is a unit of speed commonly used in countries like the United States. It's a measure of how many miles are covered in one hour of travel.
To find miles per hour, you follow a few simple steps:

• Set a number of miles traveled and divide by the number of hours it took.
• This division provides the speed in mph.

In our exercise, a car travels 220 miles in 4 hours. Dividing 220 by 4, gives 55, which means that on average, the car is moving at 55 miles per hour.
This result tells you if you continued moving at that constant speed, you'd cover 55 miles every hour. It's important to understand that mph is a way of expressing constant speed over a time.

Distance-Time Relationship

The relationship between distance and time is fundamental in calculations involving speed and travel. Knowing two of these variables allows you to compute the third, forming the basis of studying motion.
This relationship can be summarized as:

• Distance = Speed × Time
• Time = \( \frac{\text{Distance}}{\text{Speed}} \)
• Speed = \( \frac{\text{Distance}}{\text{Time}} \)

In our example, the problem was to find the speed. Given a distance of 220 miles covered in 4 hours, we applied the formula: Speed = \( \frac{220}{4} = 55 \) mph.
This relationship is crucial for planning travel, estimating arrival times, and understanding how different speeds affect travel time. By learning how these three variables interact, you gain a comprehensive understanding of motion and its implications.