/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 36 An automobile travels 220 miles ... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 36

An automobile travels 220 miles in 5 hours. Find the average rate of speed.

Short Answer

Expert verified
The average speed is 44 miles per hour.

Step by step solution

01

Identify the total distance traveled

First, we need to determine the total distance traveled by the automobile. From the problem statement, we know that the automobile travels 220 miles.
02

Determine the total time of travel

Next, we establish the total time the automobile took to travel the mentioned distance. According to the problem, the time taken is 5 hours.
03

Calculate the average speed

To find the average rate of speed, we use the formula for average speed, which is \[\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\]Substituting the given values:\[\text{Average Speed} = \frac{220 \text{ miles}}{5 \text{ hours}} = 44 \text{ miles per hour}\]
04

Express the final answer

Having computed the average speed, we conclude that the automobile's average speed is 44 miles per hour.

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Key Concepts

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

Distance Formula
When calculating average speed, it's important to grasp the distance formula, which serves as a keystone for many physics problems. Essentially, the distance formula reads: \[ \text{Distance} = \text{Rate} \times \text{Time}\] In this scenario, you're typically solving for distance when rate and time are known. However, for average speed calculations, you rearrange like this:
  • Average Speed = Total Distance / Total Time
Here, the distance formula becomes especially handy not just for finding distance when time and speed are given, but also for calculating speed. Remember to always plug in the known values carefully, ensuring consistent units for an accurate outcome.
Rate of Speed
The rate of speed represents how fast an object travels over a specific period. To simplify, you can think of speed as the distance something moves in a certain time鈥攍ike miles per hour (mph) or kilometers per hour (kph). This concept is essential for various real-world applications, from travel estimations to coordinating logistics. Understanding speed involves these aspects:
  • It is a scalar quantity, meaning it has magnitude but no direction.
  • Defined by the equation \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\).
The step-by-step approach to solving for speed often involves identifying both distance and time first, as in the original exercise. This ensures your calculations align with what's expected in various scenarios, guaranteeing a precise result.
Unit Conversion
Unit conversion is a crucial step, especially when your given values and required answers are in different measurements. Suppose your exercise calls for speed in kilometers per hour but you were provided miles per hour. Conversion becomes necessary.
Performing the correct conversions:
  • Understand the relation between units, e.g., 1 mile = 1.60934 kilometers.
  • Change miles to kilometers, time can remain if conversion is not needed.
Always double-check your answers after converting to ensure they make sense contextually. Accurate unit conversion helps maintain correctness in calculations and understanding.

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