Question
Ms. Jones is hiking. She starts at 40 feet and hikes up at a constant rate of 8 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.
Write an inequality to represent the situation. Use x to represent the number of minutes.
Answers
GPT-4o mini
To represent the situation with an inequality, we need to express Ms. Jones' elevation after hiking for \(x\) minutes. She starts at 40 feet and hikes up at a rate of 8 feet per minute. The elevation after \(x\) minutes can be expressed as:
\[
\text{Elevation} = 40 + 8x
\]
We want to determine when her elevation is above 270 feet. So, we can set up the inequality:
\[
40 + 8x > 270
\]
This inequality represents the situation and can be solved to find out how many minutes she could be hiking above 270 feet.
To solve for \(x\):
1. Subtract 40 from both sides:
\[
8x > 270 - 40
\]
\[
8x > 230
\]
2. Divide both sides by 8:
\[
x > \frac{230}{8}
\]
\[
x > 28.75
\]
This means Ms. Jones needs to hike for more than 28.75 minutes to be above 270 feet in elevation.
\[
\text{Elevation} = 40 + 8x
\]
We want to determine when her elevation is above 270 feet. So, we can set up the inequality:
\[
40 + 8x > 270
\]
This inequality represents the situation and can be solved to find out how many minutes she could be hiking above 270 feet.
To solve for \(x\):
1. Subtract 40 from both sides:
\[
8x > 270 - 40
\]
\[
8x > 230
\]
2. Divide both sides by 8:
\[
x > \frac{230}{8}
\]
\[
x > 28.75
\]
This means Ms. Jones needs to hike for more than 28.75 minutes to be above 270 feet in elevation.