An athlete runs al speed of 10 miles per hour. If one lap is 322 yards, how many laps does he run in 23 minutes? Round your answer to the nearest tenth of a lap. The athlete runs ___? laps in 28 minutes. The picture I’m sending is a example and should help a bit!!
An athlete runs al speed of 10 miles per hour. If one lap is 322 yards, how many laps does he run in 23 minutes? Round your answer to the nearest tenth of a lap. The athlete runs ___? laps in 28 minutes. The picture I’m sending is a example and should help a bit!!
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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An athlete runs al
speed of 10 miles per hour. If one lap is 322 yards, how many laps does he run in 23 minutes? Round your answer to the nearest tenth of a lap.
The athlete runs ___? laps in 28 minutes.
The picture I’m sending is a example and should help a bit!!
![## Example
### Step 1: Understand the problem.
**Key information:** The speed is 9 miles per hour. The length of one lap is 313 yards. The time is 23 minutes.
**The question:** How many laps the athlete runs in 23 minutes.
### Step 2: Devise a plan.
Use the speed and the time to find the total distance using dimensional analysis. Divide the total distance by the length of one lap to find the number of laps.
### Step 3: Execute the plan.
The athlete runs for 23 minutes. At 9 miles per hour, the total distance is calculated as follows:
\[
23 \text{ minutes} \times \frac{1 \text{ hour}}{60 \text{ minutes}} \times \frac{9 \text{ miles}}{1 \text{ hour}} = 3.45 \text{ miles} \quad \text{(Rounded to the nearest hundredth)}
\]
Use dimensional analysis again to convert miles to yards:
1 mile is equivalent to 5280 feet, and 1 yard is 3 feet.
\[
3.45 \text{ miles} \times \frac{5280 \text{ feet}}{1 \text{ mile}} \times \frac{1 \text{ yard}}{3 \text{ feet}} = 6072 \text{ yards} \quad \text{(Rounded to the nearest hundredth)}
\]
**Find the number of laps.** Round your answer to the nearest tenth of a lap.
The total distance is 6072 yards and the length of one lap is 313 yards. The number of laps is calculated as follows:
\[
\frac{6072 \text{ yards}}{313 \text{ yards per lap}} \text{ (calculate this to find the number of laps)}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12daa814-024b-4143-a208-1775681adec6%2F25079344-bea1-4c10-92b2-692bc2a379cd%2F0dasymp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Example
### Step 1: Understand the problem.
**Key information:** The speed is 9 miles per hour. The length of one lap is 313 yards. The time is 23 minutes.
**The question:** How many laps the athlete runs in 23 minutes.
### Step 2: Devise a plan.
Use the speed and the time to find the total distance using dimensional analysis. Divide the total distance by the length of one lap to find the number of laps.
### Step 3: Execute the plan.
The athlete runs for 23 minutes. At 9 miles per hour, the total distance is calculated as follows:
\[
23 \text{ minutes} \times \frac{1 \text{ hour}}{60 \text{ minutes}} \times \frac{9 \text{ miles}}{1 \text{ hour}} = 3.45 \text{ miles} \quad \text{(Rounded to the nearest hundredth)}
\]
Use dimensional analysis again to convert miles to yards:
1 mile is equivalent to 5280 feet, and 1 yard is 3 feet.
\[
3.45 \text{ miles} \times \frac{5280 \text{ feet}}{1 \text{ mile}} \times \frac{1 \text{ yard}}{3 \text{ feet}} = 6072 \text{ yards} \quad \text{(Rounded to the nearest hundredth)}
\]
**Find the number of laps.** Round your answer to the nearest tenth of a lap.
The total distance is 6072 yards and the length of one lap is 313 yards. The number of laps is calculated as follows:
\[
\frac{6072 \text{ yards}}{313 \text{ yards per lap}} \text{ (calculate this to find the number of laps)}
\]
![Certainly! Below is a transcription of the image content for use on an educational website:
---
**Example**
\[
\frac{6072 \text{ yards}}{313 \text{ yards}} = 19.4 \text{ laps (Rounded to the nearest tenth.)}
\]
**Step 4: Check your answer.**
The athlete runs 6072 yards.
**What is the length of 19.4 laps? Round your answer to the nearest yard.**
\[
19.4 \text{ laps} \times \frac{313 \text{ yards}}{\text{lap}} = 19.4 \times 313 \text{ laps} \times \text{ yards} = 6072 \text{ yards}
\]
If the speed of the athlete is 9 miles per hour and the length of one lap is 313 yards, does the athlete run 19.4 laps in 23 minutes?
**Yes.**
Therefore, the athlete runs 19.4 laps in 23 minutes.
**ANSWER:**
19.4
(End of content)
---
This example demonstrates how to calculate the number of laps an athlete runs given a specific distance and the ability to check the accuracy of the computation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12daa814-024b-4143-a208-1775681adec6%2F25079344-bea1-4c10-92b2-692bc2a379cd%2F1efb74t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Below is a transcription of the image content for use on an educational website:
---
**Example**
\[
\frac{6072 \text{ yards}}{313 \text{ yards}} = 19.4 \text{ laps (Rounded to the nearest tenth.)}
\]
**Step 4: Check your answer.**
The athlete runs 6072 yards.
**What is the length of 19.4 laps? Round your answer to the nearest yard.**
\[
19.4 \text{ laps} \times \frac{313 \text{ yards}}{\text{lap}} = 19.4 \times 313 \text{ laps} \times \text{ yards} = 6072 \text{ yards}
\]
If the speed of the athlete is 9 miles per hour and the length of one lap is 313 yards, does the athlete run 19.4 laps in 23 minutes?
**Yes.**
Therefore, the athlete runs 19.4 laps in 23 minutes.
**ANSWER:**
19.4
(End of content)
---
This example demonstrates how to calculate the number of laps an athlete runs given a specific distance and the ability to check the accuracy of the computation.
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