Question
Sarah is hiking. She starts at 80 feet and hikes up at a constant rate of 4 feet per minute. How many minutes could she be hiking if she is above 270 feet in elevation?
Write an inequality to represent the situation. Use x to represent the number of minutes.
80+4x>270
Good work!
You just wrote an inequality to represent the situation. Now solve the associated equation, 80 + 4x = 270, to find the boundary for the inequality. Show your work or solve on paper.
80 + 4x > 270
80+4x
=
270
x
=
47.5
Nice!
Now figure out if the boundary, x = 47.5, is a solution to the inequality. Does x = 47.5 make the inequality true or false?
80 + 4x > 270
True
False
Good work!
You found that x= 47.5 makes the inequality false. Now test x= 47 and x= 48. Do they make the inequality true or false?
x= 47x=47.5 (boundary)x= 4880 + 4x > 270
False
True
False
False
True
False
True
Nice!
Use the table to help you write the solution to the inequality.
x= 47x=47.5 (boundary)x= 4880 + 4x > 270FalseFalseTrue
x
>
≥
<
>
≤
Nice!
What does x> 47.5 mean in this problem?
Sarah could be hiking more than 47.5 minutes.
Sarah could be be hiking exactly 47.5 minutes or more than 47.5 minutes.
Sarah is hiking more than 47.5 feet per minute.
Write an inequality to represent the situation. Use x to represent the number of minutes.
80+4x>270
Good work!
You just wrote an inequality to represent the situation. Now solve the associated equation, 80 + 4x = 270, to find the boundary for the inequality. Show your work or solve on paper.
80 + 4x > 270
80+4x
=
270
x
=
47.5
Nice!
Now figure out if the boundary, x = 47.5, is a solution to the inequality. Does x = 47.5 make the inequality true or false?
80 + 4x > 270
True
False
Good work!
You found that x= 47.5 makes the inequality false. Now test x= 47 and x= 48. Do they make the inequality true or false?
x= 47x=47.5 (boundary)x= 4880 + 4x > 270
False
True
False
False
True
False
True
Nice!
Use the table to help you write the solution to the inequality.
x= 47x=47.5 (boundary)x= 4880 + 4x > 270FalseFalseTrue
x
>
≥
<
>
≤
Nice!
What does x> 47.5 mean in this problem?
Sarah could be hiking more than 47.5 minutes.
Sarah could be be hiking exactly 47.5 minutes or more than 47.5 minutes.
Sarah is hiking more than 47.5 feet per minute.
Answers
GPT-4o mini
The inequality \( x > 47.5 \) means that Sarah could be hiking more than 47.5 minutes. This indicates that to be above 270 feet in elevation, Sarah needs to hike for more than 47.5 minutes, but she can hike for any amount of time greater than that.
So the correct interpretation is:
**Sarah could be hiking more than 47.5 minutes.**
So the correct interpretation is:
**Sarah could be hiking more than 47.5 minutes.**