Lennon has 6 hours to spend in Ha Ha Tonka state park. He plants to drive around the park at an average speed of 20 miles per hour, looking for a good trail to hike. Once he finds a trail he likes, he will spend the remainder of his time hiking it. He hopes to travel more than 60 miles total while in the park. If he hikes at an average speed of 1.5 miles per hour, which of the following system of inequalities can be solved for the number of hours Lennon spends driving d, and the number of hours he spends hiking,h, while he is at the park?

Options

A. `1.5h+20d gt 60`
`h+d le 6`
B. `1.5h+20d gt 60`
`h+d ge 6`
C. `1.5h+20d lt 60`
`h+d ge 360`
D. `20h+1.5d gt 6`
`h+d le 60`

Answer

To solve the problem, we need to set up a system of inequalities based on the information provided about Lennon’s activities in Ha Ha Tonka State Park.

### Step-by-Step Solution:

1. **Define Variables**:
- Let \( d \) be the number of hours Lennon spends driving.
- Let \( h \) be the number of hours Lennon spends hiking.

2. **Total Time Constraint**:
- Lennon has a total of 6 hours to spend in the park. Therefore, the sum of the hours spent driving and hiking must be less than or equal to 6 hours:
\[ d + h \leq 6 \]

3. **Distance Driven and Hiked**:
- The distance driven can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- For driving at 20 miles per hour, the distance driven is:
\[ 20d \]
- For hiking at 1.5 miles per hour, the distance hiked is:
\[ 1.5h \]

4. **Total Distance Constraint**:
- Lennon hopes to travel more than 60 miles in total. Therefore, the total distance equation becomes:
\[ 20d + 1.5h > 60 \]

5. **System of Inequalities**:
- We now have the following system of inequalities:
\[ \begin{align*} 1. & \quad d + h \leq 6 \\ 2. & \quad 20d + 1.5h > 60 \end{align*} \]

6. **Conclusion**:
- The correct system of inequalities that can be solved for the number of hours Lennon spends driving \( d \) and hiking \( h \) while he is at the park is:
\[ \begin{align*} d + h \leq 6 \\ 20d + 1.5h > 60 \end{align*} \]