Problem 15 - Algebra 1

Question

In Exercises \(15-18\), find the average speed. Fly 1200 miles in 4 hours

Step-by-Step Solution

Answer

The average speed is 300 miles per hour.

Step 1: Identify the given values

The problem provides us with the total distance travelled \(1200 miles\) and the total time taken \(4 hours\).

Step 2: Apply the average speed formula

Average speed = Total distance / Total time. Plug in the given values into the formula.

Step 3: Compute the Average Speed

The total distance travelled is 1200 miles and the total time taken is 4 hours. So, Average Speed = \(1200 miles / 4 hours = 300 miles/hour\).

Key Concepts

Distance Formula

Understanding the distance formula is fundamental in calculating speed. This formula helps us determine the space covered when traveling from one point to another. In the context of speed and travel, it simplifies to:

• Distance = Speed \(\times\) Time

This means if you know how fast you are going and for how long, you can easily compute the total distance travelled. Inversely, if you have the total distance and time, you can calculate speed, as seen in the exercise above. It's about understanding these interrelated aspects: distance, speed, and time. If any two of these are known, the third can be found using the formula. This interdependency makes the distance formula very powerful in practical scenarios.

Units of Measurement

Units of measurement are crucial for clarity and precision in mathematical problems, especially in physics and real-world applications. In our exercise, distance is given in miles, and time in hours. These are standard units used in the United States. To compute speed, it's essential to ensure both distance and time are in compatible units so that the speed unit (miles per hour in this case) makes sense and remains consistent.

• Distance is typically measured in meters, kilometers, or miles.
• Time is usually measured in seconds, minutes, or hours.
• Speed can thus be measured in meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph).

In every calculation, converting units to maintain consistency is a key step. Failing to do so can lead to incorrect results and misunderstandings. Always double-check that the units are in alignment before solving any problems involving speed or distances.

Ratio and Proportion

Understanding ratio and proportion is vital when dealing with speed, distance, and time. In our example, the concept of ratio helps us see the relative relationship between the distance traveled and the time taken. The average speed is found by computing a ratio: total distance traveled over total time taken. Let’s break this down:

• A ratio compares two quantities, showing how many times one value contains another.
• A proportion is an equation that states two ratios are equal.
• Calculating an average (like average speed) often involves finding this kind of ratio.

When the total distance is divided by the total time, you effectively check how many miles are covered per hour, providing perspective on travel efficiency. Mastery of ratios and proportions can help in predicting and adjusting for different travel conditions, ensuring a deep numercal understanding of real-world problems.