Problem 78 - Elementary Algebra

Question

A fighter jet reaches a top speed of 1,316 miles per hour. How far will the jet travel if it can sustain this speed for 15 minutes?

Step-by-Step Solution

Answer

The jet will travel 329 miles.

Step 1: Convert Time to Hours

The speed of the jet is given in miles per hour (mph), so we need to express the time, 15 minutes, in hours for consistency. There are 60 minutes in an hour, so:\[\text{Time in hours} = \frac{15}{60} = 0.25 \text{ hours}\]

Step 2: Use the Speed Formula

With the time converted to hours, we can use the formula for distance which is:\[\text{Distance} = \text{Speed} \times \text{Time}\]We know the speed of the jet is 1,316 mph, and the time is 0.25 hours, so:

Step 3: Calculate the Distance

Substitute the known values into the distance formula:\[\text{Distance} = 1,316 \times 0.25\]Calculate the result:\[\text{Distance} = 329 \text{ miles}\]

Key Concepts

Understanding Speed

Speed is a measure of how fast an object moves, calculated as the distance covered per unit of time. It is commonly expressed in units like miles per hour (mph) or kilometers per hour (km/h). When dealing with problems such as the one with the fighter jet, it's crucial to first identify the speed's unit. In this case, the jet's speed is given in mph. This unit tells us how many miles the jet covers in one hour. To effectively solve any problem involving speed, it's essential to ensure that all elements are expressed in compatible units, particularly distance and time.
Identifying the speed unit helps us align our calculations correctly with the given parameters, allowing us to assess how far the jet will travel over a specific period.

Time Conversion Basics

Time conversion involves changing time from one unit of measure to another. It's a fundamental skill when dealing with speed and distance calculations. In our exercise, the speed was given in miles per hour, but the time was in minutes. To harmonize these units, we convert minutes into hours.

• There are 60 minutes in an hour.
• To convert minutes into hours, divide the number of minutes by 60.

So, for 15 minutes, the conversion to hours is:\[\text{Time in hours} = \frac{15}{60} = 0.25 \, \text{hours}\]
Being diligent about time conversion can prevent errors and ensure that your calculations are correct.

Unit Consistency Importance

Unit consistency is critical in problem-solving, especially when using formulas involving speed, distance, and time. Units must align across different measurements for the calculations to hold. For instance, if speed is in mph, the time should be in hours, and distance should be in miles.
Here's why unit consistency is vital:

• Eliminates confusion by ensuring all quantities are measured in comparable units.
• Prevents mistakes in calculations caused by mixed measurements.
• Improves clarity, making it easier to verify your work and understand problem outcomes.

Incorporating unit consistency in physics and math problems facilitates accurate and meaningful results.

Step-By-Step Calculation Process

When tackling any distance problem using the speed formula, a methodical approach can lead to success. Let's examine the steps used in our example:1. **Convert Time Units**: Start by aligning time to the speed unit by converting minutes to hours.2. **Apply the Distance Formula**: The fundamental formula for distance is: \[ \text{Distance} = \text{Speed} \times \text{Time} \]
3. **Substitute and Solve**: Insert the known values into the formula. For our fighter jet: \[ \text{Distance} = 1,316 \, \text{mph} \times 0.25 \, \text{hours} = 329 \, \text{miles} \]4. **Verify**: Always consider reviewing your steps and calculations to confirm their accuracy.
Approaching the problem step-by-step will boost your confidence in solving similar exercises and strengthen your foundational skills.