Given that Nadeem is riding at a constant speed of 10 miles per hour (mph), we can now solve for the time \( t \) using the formula:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

Since the distance Nadeem plans to ride is between 12 miles and 15 miles, the equation for time becomes:

\[
12 \leq 10 \times t \leq 15
\]

To solve for \( t \), divide the entire inequality by 10:

\[
\frac{12}{10} \leq t \leq \frac{15}{10}
\]

Simplifying this gives:

\[
1.2 \leq t \leq 1.5
\]

So, Nadeem will be riding for between 1.2 hours and 1.5 hours. 

To convert this into minutes:
- \( 1.2 \) hours is \( 1.2 \times 60 = 72 \) minutes.
- \( 1.5 \) hours is \( 1.5 \times 60 = 90 \) minutes.

Therefore, Nadeem will be riding for between 72 and 90 minutes.

Do you have any more questions, or would you like to dive deeper into any part of this?

---

Here are some related questions:
1. What if Nadeem increased her speed to 12 mph? How would that change the time?
2. How many miles would she cover if she rode for 2 hours at the same speed?
3. How does riding uphill or downhill affect the speed and time calculation?
4. If Nadeem takes a 10-minute break during her ride, how would that affect her total riding time?
5. What are the advantages of knowing the exact riding time before starting the trip?

**Tip:** It's often helpful to convert time into minutes when estimating travel duration to get a more practical sense of how long something will take.

Explore how to calculate riding time at a constant speed of 10 miles per hour (mph) using the formula Distance = Speed × Time. Understand the application of linear inequalities to determine the range of riding time based on distance constraints. Suitable for 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