Problem 7 - Prealgebra

Question

Find the distance traveled by driving at 55 miles per hour for 3 hours.

Step-by-Step Solution

Answer

The distance traveled is 165 miles.

Step 1: Understand the Formula

To find the distance traveled, we will use the basic formula for distance, which is: \[\text{Distance} = \text{Speed} \times \text{Time}\]Here, speed is given as 55 miles per hour, and time is given as 3 hours.

Step 2: Plug Values into the Formula

Substitute the given values into the distance formula: \[\text{Distance} = 55 \text{ miles per hour} \times 3 \text{ hours}\]This sets the equation up for calculation.

Step 3: Perform the Calculation

Calculate the multiplication:\[\text{Distance} = 55 \times 3 = 165\]Thus, the distance traveled is 165 miles.

Key Concepts

Distance Formula

The distance formula is an essential tool when trying to determine how far an object has traveled. It is expressed as \( \text{Distance} = \text{Speed} \times \text{Time} \). This means that the distance someone or something travels can be calculated by multiplying their speed by the time they are traveling at that speed.

In simpler terms:

• "Speed" is how fast you are moving. For example, 55 miles per hour.
• "Time" refers to how long you are traveling. For example, 3 hours.
• "Distance" tells you how far you traveled in total.

By using this formula, you can easily determine the total distance traveled if the speed and time are known. It's quite handy if you want to plan a road trip or track how far you've gone.

Speed and Time Relationship

Speed and time are closely related when it comes to understanding movement and distance. Their relationship helps you predict or determine travel outcomes.

If you think of speed as how fast you are going, then time is how long you maintain that speed. Both factors directly affect the distance covered:

• If either your speed or your travel time increases, the distance you can travel also increases.
• If you travel slower, or your travel time decreases, you'd end up covering less distance.

This relationship is straightforward: multiply speed and time, and you will determine the traveled distance. It's also very intuitive—imagine traveling faster but for the same amount of time, and seeing how you end up further down the road.

Problem-Solving Steps

Facing a mathematical problem can seem daunting, but breaking it into steps makes it manageable. Consider the given problem of calculating distance as an example:

First, understand the formula you'll use. In this case, distance equals speed times time. With this equation in mind, identify the problem's components—speed, which is 55 miles per hour, and time, 3 hours.

Next, plug the known values into the formula. This involves substituting the given speed and time into the equation, which looks like: \( \text{Distance} = 55 \times 3 \). This makes sure you're set up for the correct calculation.

Finally, perform the calculation to find the answer. Multiply the numbers (55 and 3) to get 165. This is your total traveled distance, shown through simple arithmetic.

By following these organized steps—understanding the formula, substituting values, and calculating—you simplify what once seemed a complex problem. It's a strategy worth remembering for future exercises!