Question

Alexandria wants to go hiking on Saturday. She will consider these conditions when she chooses which of several parks to visit: • She wants to hike for 2 hours. • She wants to spend no more than 6 hours away from home. • She can average 65 miles per hour to and from the park. Write and solve an inequality to find possible distances from Alexandria’s home to a park that satisfies the conditions.

Answer 1

The important thing to consider here is the maximum amount of time she can spend driving. Since she will spend 2 hours at the park and want to be gone no more than 6 hours, this number is 4 hours.
This means she can spend 2 hours on the way to the park and 2 hours back. Her maximum distance, therefore, is 2 hours times an average speed of 65 miles per hour
Therefore:
2x ≤65 * 4
2x ≤ 260
x ≤ 130
Her maximum distance is 2 hours x 65 mph = 130 miles.

Answer 2

Alexandria can choose any distance not more than 130 miles from her house to the park.

Explanation:

Let Alexandria takes time 't' hours to walk from home to the park and distance between park and home is 'x' miles.

If she averages 65 miles per hour "to and fro" from her home to the park then the inequality that will represent this situation will be

2x ≤ 65t [ Distance = Speed × time ]

If she wants to hike for 2 hours and maximum time spent to reach the park is 6 hours

Then the maximum time spent by her to reach the park from her home should be = 6 - 2 = 4 hours.

By placing the value of t = 4 in the inequality

2x ≤ (65×4)

2x ≤ 260

x ≤ 130

Therefore, Alexandria can choose any distance not more than 130 miles from her house to the park.