Problem 71 - Algebra 1

Question

If you are driving at a constant speed of 68 miles per hour, how long will it take you to travel 170 miles? (Review 1.1 )

Step-by-Step Solution

Answer

Therefore, it will take 2.5 hours to travel 170 miles at a speed of 68 miles per hour.

Step 1 Identification

Identify that the exercise involves the motion physics and it can be solved with the formula of time distance relationship T=D/S. Here, D = 170 miles and S = 68 miles per hour.

Step 2 Calculations

Calculate the time it takes to travel the distance by substituting D and S into the formula. So, T = 170 miles / 68 miles per hour

Step 3 Simplification

Simplify the calculation to get the exact time. Therefore, T = 2.5 hours

Key Concepts

Understanding Motion Physics

Motion physics is fundamental in our understanding of how objects move. The core concept revolves around three primary elements: distance, speed, and time. When an object moves, it covers a certain distance over a specific period. This interplay forms the foundation of motion physics. To predict or calculate how long something takes to move from one place to another, we use these relations. The basic formula connecting them is:
\( T = \frac{D}{S} \)
where \( T \) stands for time, \( D \) is distance, and \( S \) is speed. This formula helps us calculate one of the variables when the other two are known. Thus, motion physics helps us not only to answer practical questions like how long a trip will take, but also to understand the movement dynamics in various scientific contexts.

The Concept of Constant Speed

The concept of constant speed is crucial to many problems involving motion. When an object moves at constant speed, it means that the rate at which it travels does not change over time. This simplification allows us to use straightforward calculations to predict motion. Constant speed implies that:

• The speed remains the same throughout the entire journey
• The object covers equal distances in equal intervals of time
• No additional forces are causing acceleration or deceleration

For example, if you drive at a constant speed of 68 miles per hour, the distance you travel each hour remains consistent. This uniformity greatly simplifies calculations, allowing you to reliably predict how long a journey will take if you maintain a consistent speed.

Calculating Travel Time

Travel time calculation is a practical application of the time-distance relationship formula. To determine how long a journey will take, you need to know the total distance and the speed at which you will travel. Using the formula \( T = \frac{D}{S} \):

• \( D \) is the total distance to travel
• \( S \) is the constant speed

Substituting these into the formula, you can calculate \( T \), the time required for the journey.
For instance, if you're driving 170 miles at a constant speed of 68 miles per hour:
Substitute in the values to get \( T = \frac{170}{68} \), which simplifies to \( T = 2.5 \) hours.
This means it will take 2.5 hours to complete the trip. This calculation is essential for planning travel, ensuring you know how long you will be on the road.