Melinda And Paula Shovel Driveways And Sidewalks In The Winter As A Way To Earn Extra Money. Together, They Shoveled 450 Square Feet Of Sidewalk In 30 Minutes. Then Melinda Shoveled For 20 Minutes While Paula Shoveled For 25 Minutes To Complete 345
Introduction
As the winter months approach, many people are looking for ways to earn extra money. For Melinda and Paula, shoveling driveways and sidewalks is a great way to do just that. In this article, we will explore their shoveling challenge and use mathematical concepts to analyze their work.
The Initial Shoveling Challenge
Melinda and Paula started their shoveling challenge by working together to clear 450 square feet of sidewalk in just 30 minutes. This impressive feat showcases their teamwork and physical endurance. But how did they manage to complete this task so quickly?
Calculating Their Combined Rate
To understand their combined rate, we need to calculate the number of square feet they shoveled per minute. We can do this by dividing the total square feet shoveled (450) by the total time taken (30 minutes).
Combined rate = Total square feet / Total time
= 450 square feet / 30 minutes
= 15 square feet per minute
This means that together, Melinda and Paula can shovel 15 square feet of sidewalk per minute.
The Second Shoveling Challenge
After completing the initial challenge, Melinda and Paula decided to work individually to clear the remaining sidewalk. Melinda shoveled for 20 minutes, while Paula shoveled for 25 minutes. Together, they completed 345 square feet of sidewalk.
Calculating Melinda's Rate
To calculate Melinda's rate, we need to divide the total square feet she shoveled (345) by the time she took (20 minutes).
Melinda's rate = Total square feet / Time taken
= 345 square feet / 20 minutes
= 17.25 square feet per minute
This means that Melinda can shovel 17.25 square feet of sidewalk per minute.
Calculating Paula's Rate
To calculate Paula's rate, we need to divide the total square feet she shoveled (345) by the time she took (25 minutes).
Paula's rate = Total square feet / Time taken
= 345 square feet / 25 minutes
= 13.8 square feet per minute
This means that Paula can shovel 13.8 square feet of sidewalk per minute.
Comparing Their Rates
Now that we have calculated their individual rates, let's compare them to their combined rate.
Combined rate = 15 square feet per minute
Melinda's rate = 17.25 square feet per minute
Paula's rate = 13.8 square feet per minute
We can see that Melinda's rate is higher than their combined rate, while Paula's rate is lower. This suggests that Melinda is the more efficient shoveler, and Paula is the less efficient shoveler.
Conclusion
In conclusion, Melinda and Paula's shoveling challenge is a great example of how mathematical concepts can be applied to real-world situations. By calculating their combined rate and individual rates, we can gain a better understanding of their physical abilities and teamwork. Whether you're a math enthusiast or just looking for ways to earn extra money, this article has shown that math can be a valuable tool in many different contexts.
Additional Questions
- If Melinda and Paula worked together for 40 minutes, how many square feet of sidewalk would they be able to clear?
- If Melinda's rate increases by 10% and Paula's rate decreases by 10%, how would their combined rate change?
- If Melinda and Paula worked individually for 30 minutes each, how many square feet of sidewalk would they be able to clear?
Answer Key
- If Melinda and Paula worked together for 40 minutes, they would be able to clear 20 square feet per minute (combined rate) x 40 minutes = 800 square feet.
- If Melinda's rate increases by 10% and Paula's rate decreases by 10%, their combined rate would change as follows:
- Melinda's rate: 17.25 x 1.10 = 19.025 square feet per minute
- Paula's rate: 13.8 x 0.90 = 12.48 square feet per minute
- Combined rate: 19.025 + 12.48 = 31.505 square feet per minute
- If Melinda and Paula worked individually for 30 minutes each, they would be able to clear:
- Melinda: 17.25 x 30 = 517.5 square feet
- Paula: 13.8 x 30 = 414 square feet
Melinda and Paula's Shoveling Challenge: Q&A =====================================================
Introduction
In our previous article, we explored Melinda and Paula's shoveling challenge and used mathematical concepts to analyze their work. In this article, we will answer some of the most frequently asked questions about their shoveling challenge.
Q: How did Melinda and Paula manage to clear 450 square feet of sidewalk in just 30 minutes?
A: Melinda and Paula's combined rate was 15 square feet per minute, which means they were able to clear 15 square feet of sidewalk per minute. By working together, they were able to maintain this rate and clear the entire sidewalk in 30 minutes.
Q: What is Melinda's rate of shoveling?
A: Melinda's rate of shoveling is 17.25 square feet per minute. This means that she is able to clear 17.25 square feet of sidewalk per minute.
Q: What is Paula's rate of shoveling?
A: Paula's rate of shoveling is 13.8 square feet per minute. This means that she is able to clear 13.8 square feet of sidewalk per minute.
Q: How does Melinda's rate compare to Paula's rate?
A: Melinda's rate is higher than Paula's rate. This means that Melinda is the more efficient shoveler, and Paula is the less efficient shoveler.
Q: If Melinda and Paula worked together for 40 minutes, how many square feet of sidewalk would they be able to clear?
A: If Melinda and Paula worked together for 40 minutes, they would be able to clear 20 square feet per minute (combined rate) x 40 minutes = 800 square feet.
Q: If Melinda's rate increases by 10% and Paula's rate decreases by 10%, how would their combined rate change?
A: If Melinda's rate increases by 10% and Paula's rate decreases by 10%, their combined rate would change as follows:
- Melinda's rate: 17.25 x 1.10 = 19.025 square feet per minute
- Paula's rate: 13.8 x 0.90 = 12.48 square feet per minute
- Combined rate: 19.025 + 12.48 = 31.505 square feet per minute
Q: If Melinda and Paula worked individually for 30 minutes each, how many square feet of sidewalk would they be able to clear?
A: If Melinda and Paula worked individually for 30 minutes each, they would be able to clear:
- Melinda: 17.25 x 30 = 517.5 square feet
- Paula: 13.8 x 30 = 414 square feet
Q: What is the most efficient way for Melinda and Paula to clear the sidewalk?
A: The most efficient way for Melinda and Paula to clear the sidewalk is for them to work together. By combining their rates, they are able to clear the sidewalk more quickly and efficiently than if they were to work individually.
Q: How can Melinda and Paula improve their shoveling rates?
A: Melinda and Paula can improve their shoveling rates by practicing and working together more efficiently. They can also try to increase their physical endurance and strength to shovel more square feet per minute.
Conclusion
In conclusion, Melinda and Paula's shoveling challenge is a great example of how mathematical concepts can be applied to real-world situations. By answering these frequently asked questions, we can gain a better understanding of their shoveling challenge and how they can improve their rates. Whether you're a math enthusiast or just looking for ways to earn extra money, this article has shown that math can be a valuable tool in many different contexts.