5.
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.

A. 392 miles
B. 260 miles
C. 16 miles
D. 392 miles

Answer:

B. 260 miles

Step-by-step explanation:

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:

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

Step-by-step 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.

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.

The actual answer is 180 miles if anyone was wondering. I know the other answer is "Verified" but its wrong. me and the other people who trusted it know that. good luck.

Alexandria wants to go hiking on Saturday. To choose from several parks she could go to, she considers these conditions.  

She wants to hike for 2 hours.

She wants to spend no more than 6 hours away home.

She can average 65 miles per hour to and from the park.

Write and solve an inequality to find possible distances from Alexandrias home to a park that satisfies the conditions.

Explain show work please.

Favorite Answer

The distance from Alexandria's home to a park has to be within 130 miles.

Let h = time of Alexandria's hike = 2 hours.

Let p = time spent to get to park (driving)

h + 2p (since it is round trip - to the park and back) <= 6 hours (time to spend away from home)

h = 2, thus

2 + 2p <= 6

2p <= 4

p <= 4/2 = 2

Thus, she has to spend 2 hours to get to the park, and spend 2 hours to get back home.

distance to the park <= speed of driving x time of getting to park

                             <= 65 miles per hour x 2 hours

                             <= 130 miles

Thus, we get the 130 miles.

The correct option is B. 260 miles. and the required inequality is [tex]2+\dfrac{D}{65} \leq 6[/tex].

Given, Alexandria wants to go hiking based on the conditions.

The average speed of Alexandria is 65 miles per hour.

Since she wants to hike minimum of 2 hours, so minimum distance covered by her will be  [tex](65\times2=130) \\[/tex] miles.

Now time [tex]t[/tex] required to cover [tex]D[/tex] distance with the speed of 65 miles per hour will be  [tex]\frac{D}{65}[/tex] hours.

But She doesn't want to spend more than 6 hours away from home,

So the inequality becomes,

[tex]2+\dfrac{D}{65} \leq 6[/tex].

On solving for D,

[tex]\dfrac{D}{65} \leq 6-2[/tex]

[tex]D\leq 4\times65\\\\\D\leq 260[/tex]

Hence the Distance traveled by Alexandria must not exceed by 260 miles.

Therefore the correct option is B. 260 miles. and the required inequality is [tex]2+\dfrac{D}{65} \leq 6[/tex].

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