College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip?
**Solution:**
To find the average speed, use the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
1. **Calculate the time for each segment of the trip:**
- For the first 4 miles at 30 mi/hr:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{4 \text{ miles}}{30 \text{ mi/hr}} = \frac{2}{15} \text{ hours}
\]
- For the second 4 miles at 50 mi/hr:
\[
\text{Time} = \frac{4 \text{ miles}}{50 \text{ mi/hr}} = \frac{4}{50} \text{ hours} = \frac{2}{25} \text{ hours}
\]
2. **Calculate the total time for the trip:**
\[
\text{Total Time} = \frac{2}{15} \text{ hours} + \frac{2}{25} \text{ hours}
\]
Find a common denominator (75):
\[
\frac{10}{75} + \frac{6}{75} = \frac{16}{75} \text{ hours}
\]
3. **Calculate the average speed:**
\[
\text{Average Speed} = \frac{8 \text{ miles}}{\frac{16}{75} \text{ hours}} = 8 \times \frac{75}{16} = \frac{600}{16} = 37.5 \text{ mi/hr}
\]
Thus, the average speed for the whole 8-mile trip is **37.5 mi/hr**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecd1cfe6-c66d-4560-847c-08cc62f7911e%2F2c4bfe98-a038-481f-b43f-25dfe33e741f%2F5yj79ii_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip?
**Solution:**
To find the average speed, use the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
1. **Calculate the time for each segment of the trip:**
- For the first 4 miles at 30 mi/hr:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{4 \text{ miles}}{30 \text{ mi/hr}} = \frac{2}{15} \text{ hours}
\]
- For the second 4 miles at 50 mi/hr:
\[
\text{Time} = \frac{4 \text{ miles}}{50 \text{ mi/hr}} = \frac{4}{50} \text{ hours} = \frac{2}{25} \text{ hours}
\]
2. **Calculate the total time for the trip:**
\[
\text{Total Time} = \frac{2}{15} \text{ hours} + \frac{2}{25} \text{ hours}
\]
Find a common denominator (75):
\[
\frac{10}{75} + \frac{6}{75} = \frac{16}{75} \text{ hours}
\]
3. **Calculate the average speed:**
\[
\text{Average Speed} = \frac{8 \text{ miles}}{\frac{16}{75} \text{ hours}} = 8 \times \frac{75}{16} = \frac{600}{16} = 37.5 \text{ mi/hr}
\]
Thus, the average speed for the whole 8-mile trip is **37.5 mi/hr**.
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