Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![**Problem Statement:**
Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 330 miles in the same time that Dana travels 300 miles. If Chuck's rate of travel is 5 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?
**Explanation:**
To solve this problem, we need to establish a relationship between the distances traveled, the time taken, and their speeds. Let's denote Dana's speed as \( v \) mph. Therefore, Chuck's speed will be \( v + 5 \) mph.
Using the formula for time:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
We have the following equations based on the problem statement:
- For Dana:
\[
t = \frac{300}{v}
\]
- For Chuck:
\[
t = \frac{330}{v + 5}
\]
Since they travel for the same length of time (\( t \)), we can equate the two expressions:
\[
\frac{300}{v} = \frac{330}{v + 5}
\]
Solving this equation will give us the value of \( v \), and subsequently, Chuck's speed can be calculated as \( v + 5 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50a25d79-a0e0-4f16-9259-569d4f27b8fc%2F796068c2-b65b-48ad-b8c9-90c4b79bf619%2Fy1vtd5s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 330 miles in the same time that Dana travels 300 miles. If Chuck's rate of travel is 5 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?
**Explanation:**
To solve this problem, we need to establish a relationship between the distances traveled, the time taken, and their speeds. Let's denote Dana's speed as \( v \) mph. Therefore, Chuck's speed will be \( v + 5 \) mph.
Using the formula for time:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
We have the following equations based on the problem statement:
- For Dana:
\[
t = \frac{300}{v}
\]
- For Chuck:
\[
t = \frac{330}{v + 5}
\]
Since they travel for the same length of time (\( t \)), we can equate the two expressions:
\[
\frac{300}{v} = \frac{330}{v + 5}
\]
Solving this equation will give us the value of \( v \), and subsequently, Chuck's speed can be calculated as \( v + 5 \).
Expert Solution
Step 1
Speed , distance and Time:
Speed=
Chuck travel 330 miles in the time it takes Dana to travel 300 miles.
If Chucks rate is 5 mph more than Danas, and they travel the same length of time.
Let Chuck's speed=s
Dana's speed =s-5
the times are equal, so we can write
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