Solve an inequality to determine how many hours it would take to walk 21 miles if I was walking 3 1/2 miles an hour

To solve this inequality, we need to determine how many hours \( t \) it would take to walk 21 miles at a speed of \( 3\frac{1}{2} \) miles per hour.

### Step-by-Step Solution:

1. Let \( t \) represent the number of hours it takes to walk 21 miles.
2. The total distance walked is given by the product of time and speed:
   \[
   \text{Distance} = \text{Speed} \times \text{Time}
   \]
   In this case:
   \[
   21 \leq \left(3 \frac{1}{2}\right) \times t
   \]
3. Convert \( 3\frac{1}{2} \) to an improper fraction:
   \[
   3 \frac{1}{2} = \frac{7}{2}
   \]
   So the inequality becomes:
   \[
   21 \leq \frac{7}{2} \times t
   \]
4. To eliminate the fraction, multiply both sides of the inequality by 2:
   \[
   42 \leq 7t
   \]
5. Solve for \( t \) by dividing both sides by 7:
   \[
   t \geq \frac{42}{7}
   \]
   \[
   t \geq 6
   \]

### Conclusion:
It would take at least 6 hours to walk 21 miles if you are walking at a speed of 3 1/2 miles per hour.

Would you like further clarification on this, or any additional details?

### Related Questions:
1. What if the walking speed was 4 miles per hour? How would that change the time?
2. How long would it take to walk 15 miles at the same speed?
3. What if you walk for only 5 hours, how far would you travel at 3 1/2 miles per hour?
4. How would the time change if you added a break after every 2 hours?
5. How many miles could you walk in 10 hours at a speed of 3 1/2 miles per hour?

### Tip:
Always convert mixed numbers to improper fractions for easier calculation in problems like this one!

Solve an inequality to determine how many hours it would take to walk 21 miles if I was walking 3 1/2 miles an hour.

Learn how to solve an inequality to determine the time required to walk 21 miles at a speed of 3 1/2 miles per hour. This step-by-step solution covers key concepts such as inequalities, rates, and fractions. Suitable for students in Grades 6-8.

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