Problem 57 - Algebra 1: Concepts and Skills

Question

It takes you 3 hours to drive to your friend's house at an average speed of 48 miles per hour. How far did you travel?

Step-by-Step Solution

Answer

The distance traveled was 144 miles.

Step 1: Understand the formula.

The formula for calculating distance is distance = speed × time.

Step 2: Substitute the given values into the formula.

Substitute the given speed (48 mph) and time duration (3 hours) into the formula: distance = 48 miles/hour × 3 hours.

Step 3: Perform the multiplication.

Multiply the speed and time to get the distance: distance = 144 miles.

Key Concepts

Understanding Average Speed

Average speed is a fundamental concept when it comes to calculating distances over time. It tells us how fast something is moving on average over a certain period of time. In simple terms, average speed is like saying, "If I kept moving at a constant pace, how fast would that be?"
Average speed is calculated by the formula:

• Average speed = Total distance traveled / Total time taken

For example, in the exercise, you cover a certain distance at an average speed of 48 miles per hour. This means, if your speed were constant throughout, you would cover 48 miles for every hour spent traveling. Understanding average speed is crucial, especially when distances and times vary throughout a journey.

Calculating Time for a Journey

Time calculation is essential to determine how long a journey will take given a specific speed or to figure out how long you have already traveled. In the exercise, you're given the time directly, but knowing how to find this is useful in different problems.
When you need to find time, the formula rearranges to:

• Time = Distance / Speed

This formula helps answer questions such as: "How long will it take to travel 100 miles at an average speed of 50 miles per hour?" By using the formula:

• Time = 100 miles / 50 miles per hour = 2 hours

This shows it would take 2 hours to travel that distance. Remembering this relationship between time, speed, and distance makes solving travel-related problems much simpler.

Multiplication in Algebra

When solving algebraic expressions, multiplication is often a quick yet crucial step to finding the answer. In the context of this exercise, once you have the speed and time, you simply multiply them to find the distance.
The formula for distance is:

• Distance = Speed × Time

In our example, you multiply 48 miles per hour by 3 hours. When you break down the multiplication step:

• 48 × 3 = 144

This tells us the total distance traveled is 144 miles. Understanding how to use multiplication in algebraic formulas like these is vital for solving equations quickly and accurately. Multiplication allows you to combine variables and constants efficiently to find the desired result.