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Chapter 2: Problem 3

Solve each problem. Tri Phong traveled from Chicago to Des Moines, a distance of \(300 \mathrm{mi}\), in \(10 \mathrm{hr}\). What was his rate in miles per hour?

Short Answer

Expert verified
His rate was 30 miles per hour.

Step by step solution

01

Write Down the Formula

To find the rate (speed) in miles per hour, use the formula: \[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} \]
02

Identify the Given Values

Identify the values that are given in the problem. Here, the distance is \(300 \text{ miles}\) and the time is \(10 \text{ hours}\).
03

Plug in the Values

Substitute the given values into the formula: \[ \text{Rate} = \frac{300 \text{ miles}}{10 \text{ hours}} \]
04

Simplify the Fraction

Simplify the fraction to find the rate: \[ \text{Rate} = \frac{300}{10} = 30 \text{ miles per hour} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distance-Time Relationship
Understanding the distance-time relationship is crucial when calculating speed. This relationship is based on the simple equation:
  • Speed (or Rate) = Distance / Time
This formula shows that speed is a measure of how much distance is covered in a specific amount of time.
Imagine you're on a road trip. If you know how far you've traveled and how long it took, you can easily find out your speed.
The distance-time formula helps you with that.
This makes it easier to understand how fast or slow you're going.
In our case of Tri Phong's trip:
  • Distance = 300 miles
  • Time = 10 hours
By plugging these values into the formula, you can find out the speed.
Miles Per Hour
Miles per hour (mph) is a common unit for measuring speed. It tells you how many miles you travel in one hour.
For example, if a car's speed is 60 mph, it means the car travels 60 miles in one hour.
In our case, we need to find Tri Phong's speed in miles per hour.
This involves dividing the distance traveled by the time taken.
  • For Tri Phong's trip:
    Rate = 300 miles / 10 hours
  • This simplifies to 30 miles per hour
So, Tri Phong traveled at a speed of 30 miles per hour. Knowing the speed helps in planning similar trips and understanding travel times.
Fraction Simplification
Fraction simplification is a key step in solving rate problems. It's important to break down complex fractions into simpler terms.
In our example:
  • The formula Rate = Distance / Time gave us Rate = 300 miles / 10 hours
  • To simplify this fraction, we divide both the numerator (300) and the denominator (10) by their greatest common divisor, which is 10.
  • This simplifies the fraction to 30/1 or 30 miles per hour
Simplifying fractions makes it easier to understand and work with rates.
It's a valuable skill that applies not only to speed problems but also to many real-life scenarios.
With practice, simplifying fractions becomes second nature.

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