Problem 39 - Algebra 1

Question

If you are driving at a constant speed of 96 kilometers per hour, how long will it take you to travel 288 kilometers?

Step-by-Step Solution

Answer

It will take 3 hours to travel 288 kilometers at a constant speed of 96 kilometers per hour.

Step 1: Write down given values

From the problem, we have distance \(d = 288\) kilometers and speed \(s = 96\) kilometers per hour.

Step 2: Write down the time formula

The formula to calculate time is, \(t = d \u00F7 s\). Where: \n - \(t\) is the time \n - \(d\) is the distance \n - \(s\) is the speed.

Step 3: Substitute given values into the formula

Substituting the given variables into the formula gives \(t = 288 \u00F7 96\).

Step 4: Solve the equation

After solving the equation, we find that \(t = 3\)

Key Concepts

Solving Equations

When faced with a problem, such as determining how long a trip will take, writing an equation is often a good first step. In mathematics, equations help us find unknown values when we are given specific data. The equation from the exercise is based on a straightforward formula:

• \( t = \frac{d}{s} \)

Here, \( t \) represents time, \( d \) is the distance, and \( s \) indicates speed. This equation essentially states that time is the distance divided by speed.
Understanding how to rearrange formulas and plug in values can help you solve similar problems. Once you have your values, substitute them into the equation. For example, with a distance \( d = 288 \) kilometers and speed \( s = 96 \) kilometers per hour, the equation becomes:

• \( t = \frac{288}{96} \)

The result will give you the time it takes to travel the specified distance.

Constant Speed

The notion of constant speed is crucial in understanding how travel calculations work. When an object moves at constant speed, it means that it covers equal distances in equal times without any change in velocity. This simplification is what allowed us to use the formula \( t = \frac{d}{s} \) directly.
The speed value of 96 kilometers per hour in our problem signifies a constant rate at which the vehicle travels. No acceleration or deceleration is involved, which keeps the calculations straightforward. Knowing that the speed won’t vary helps ensure that the results from the time-distance-speed formula remain valid throughout the trip.

• Constant speed implies no need to account for stops or changes in speed.
• It simplifies calculations by allowing a direct application of the distance-time relationship.

Understanding this concept is pivotal when dealing with problems involving distance covered over time.

Distance Calculation

Determining the distance traveled or managing travel calculations often involves utilizing the formula relating distance, speed, and time. This relationship is grounded in the basic principle:

• Distance = Speed × Time

In the given problem, this principle was rearranged to solve for time, resulting in the equation \( t = \frac{d}{s} \).
Grasping this concept unlocks a variety of applications. For instance, if you know the time and speed, you can determine the distance traveled by rearranging the formula to \( d = s \times t \). Similarly, if you're aware of both distance and time, speed can be found by using \( s = \frac{d}{t} \).
This foundational formula provides the framework to tackle numerous problems in real life and academia, expanding beyond travel calculations to understand any movement-based situations.