https://file.aiquickdraw.com/mathbot/file/1725490665854mtepxmm2.jpg

It seems you've uploaded an image containing a math problem. I will extract the text and help solve it.

Here’s the text from the image:

**Question:**
Daniel ran 4 miles in 30 minutes. Shelby ran 7 miles in 60 minutes. After running, Shelby said that she ran faster than Daniel. Using their rates in miles per minute, how many times faster did Shelby run than Daniel?

Answer choices:
A. \( \frac{7}{2} \)
B. \( \frac{7}{3} \)
C. \( \frac{7}{4} \)
D. \( \frac{7}{5} \)
E. \( \frac{7}{6} \)

---

### Solution:

1. **Find Daniel's rate**: Daniel ran 4 miles in 30 minutes.
   \[
   \text{Daniel's rate} = \frac{4 \text{ miles}}{30 \text{ minutes}} = \frac{4}{30} = \frac{2}{15} \text{ miles per minute}
   \]

2. **Find Shelby's rate**: Shelby ran 7 miles in 60 minutes.
   \[
   \text{Shelby's rate} = \frac{7 \text{ miles}}{60 \text{ minutes}} = \frac{7}{60} \text{ miles per minute}
   \]

3. **Find how many times faster Shelby ran**: We need to compare Shelby's rate to Daniel's rate by dividing Shelby's rate by Daniel's rate:
   \[
   \text{Comparison} = \frac{\frac{7}{60}}{\frac{2}{15}} = \frac{7}{60} \times \frac{15}{2} = \frac{7 \times 15}{60 \times 2} = \frac{105}{120} = \frac{7}{8}
   \]

Thus, Shelby ran at \(\frac{7}{8}\) of Daniel's speed, which means she did not actually run faster than him! Therefore, none of the answer choices seem to be applicable if we look at the interpretation of running faster.

Would you like further clarification, or should I adjust based on any possible missing details from the question?

---

Here are 5 related questions to explore this topic further:

1. How do you convert a rate from miles per minute to miles per hour?
2. If Daniel ran 4 miles in 25 minutes, how much faster is Shelby than him?
3. What is the importance of using unit rates to compare speeds or rates of work?
4. If Shelby ran at \( \frac{7}{5} \) miles per minute, how many miles would she run in 50 minutes?
5. How do you compare speeds when given different time intervals and distances?

**Tip:** Always simplify rates or ratios when comparing two quantities to ensure accuracy.

Daniel ran 4 miles in 30 minutes. Shelby ran 7 miles in 60 minutes. After running, Shelby said that she ran faster than Daniel. Using their rates in miles per minute, how many times faster did Shelby run than Daniel?
Answer choices:
A. \( \frac{7}{2} \)
B. \( \frac{7}{3} \)
C. \( \frac{7}{4} \)
D. \( \frac{7}{5} \)
E. \( \frac{7}{6} \)

Learn how to compare rates to determine how many times faster Shelby ran than Daniel. This problem involves calculating and comparing rates using the formula Rate = Distance / Time. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation