A cyclist traveled 20 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 80 kilometers, the skater had gone 30 kilometers. Find the speed of the skater.
A cyclist traveled 20 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 80 kilometers, the skater had gone 30 kilometers. Find the speed of the skater.
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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![### Solving a Distance, Rate, Time Problem Using a Rational Equation
#### Problem Statement:
A cyclist traveled 20 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 80 kilometers, the skater had gone 30 kilometers. Find the speed of the skater.
#### Solution:
To find the speed of the skater, we start by setting up an equation based on the relationship between distance, rate, and time.
Let \( x \) represent the speed of the skater in kilometers per hour (km/h).
The speed of the cyclist is \( x + 20 \) km/h.
Since both the cyclist and the skater travel for the same amount of time, we can use the time formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Based on the given information:
- Time for the skater: \( \frac{30}{x} \)
- Time for the cyclist: \( \frac{80}{x+20} \)
Set the times equal to each other:
\[
\frac{30}{x} = \frac{80}{x + 20}
\]
Solve this equation to find the value of \( x \). This will give you the speed of the skater.
#### Explanation Tool:
An explanation and check options are available to verify the computed speed of the skater.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1fcac1b-f2a3-49f7-a72a-fa5828574f4f%2F173b9741-4397-46be-a9bf-c2606a4ea054%2F04rnr9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving a Distance, Rate, Time Problem Using a Rational Equation
#### Problem Statement:
A cyclist traveled 20 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 80 kilometers, the skater had gone 30 kilometers. Find the speed of the skater.
#### Solution:
To find the speed of the skater, we start by setting up an equation based on the relationship between distance, rate, and time.
Let \( x \) represent the speed of the skater in kilometers per hour (km/h).
The speed of the cyclist is \( x + 20 \) km/h.
Since both the cyclist and the skater travel for the same amount of time, we can use the time formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Based on the given information:
- Time for the skater: \( \frac{30}{x} \)
- Time for the cyclist: \( \frac{80}{x+20} \)
Set the times equal to each other:
\[
\frac{30}{x} = \frac{80}{x + 20}
\]
Solve this equation to find the value of \( x \). This will give you the speed of the skater.
#### Explanation Tool:
An explanation and check options are available to verify the computed speed of the skater.
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