Question
a hiker has already hiked 2 miles. they walk at a pace of 5 miles every 2 hours. select the graph that shows how far the hiker will hike over time.
a. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 10 in 1 unit increments and the y-axis labeled as miles ranging from 0 to 10 in 1 unit increments. Two unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 7 right parenthesis. A solid arrow passes through these points.
b. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 10 in 1 unit increments and the y-axis labeled as miles ranging from 0 to 30 in increments of 5. Four unlabeled points are plotted as follows: left parenthesis 0 comma 5 right parenthesis, left parenthesis 2 comma 10 right parenthesis, left parenthesis 4 comma 15 right parenthesis, and left parenthesis 6 comma 20 right parenthesis. A solid arrow passes through these points.
a. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 10 in 1 unit increments and the y-axis labeled as miles ranging from 0 to 10 in 1 unit increments. Two unlabeled points are plotted as follows: left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 7 right parenthesis. A solid arrow passes through these points.
b. A coordinate graph shows the x-axis labeled as hours ranging from 0 to 10 in 1 unit increments and the y-axis labeled as miles ranging from 0 to 30 in increments of 5. Four unlabeled points are plotted as follows: left parenthesis 0 comma 5 right parenthesis, left parenthesis 2 comma 10 right parenthesis, left parenthesis 4 comma 15 right parenthesis, and left parenthesis 6 comma 20 right parenthesis. A solid arrow passes through these points.
Answers
GPT-4o mini
To determine which graph represents the hiker's distance over time, we need to calculate how far the hiker hikes over time given the starting distance and their walking pace.
Given information:
- The hiker has already hiked 2 miles.
- The hiker walks at a pace of 5 miles every 2 hours.
From the pace, we can find the rate:
- 5 miles in 2 hours means the hiker walks at a rate of \( \frac{5 \text{ miles}}{2 \text{ hours}} = 2.5 \text{ miles per hour}\).
Now, let's analyze the hiker's distance over time starting from the 2 miles they've already completed.
At time \( t = 0 \) hours, the hiker has traveled 2 miles.
From this point on:
- After 1 hour: \( 2 \text{ miles} + (2.5 \text{ miles/hour} \times 1 \text{ hour}) = 2 + 2.5 = 4.5 \text{ miles} \)
- After 2 hours: \( 2 \text{ miles} + (2.5 \text{ miles/hour} \times 2 \text{ hours}) = 2 + 5 = 7 \text{ miles} \)
- After 4 hours: \( 2 \text{ miles} + (2.5 \text{ miles/hour} \times 4 \text{ hours}) = 2 + 10 = 12 \text{ miles} \)
- After 6 hours: \( 2 \text{ miles} + (2.5 \text{ miles/hour} \times 6 \text{ hours}) = 2 + 15 = 17 \text{ miles} \)
Now, we can look at the options:
**Option A** provides the points:
- (0, 2) and (2, 7)
**Option B** provides the points:
- (0, 5), (2, 10), (4, 15), and (6, 20)
Based on our calculations:
- At \( t = 0 \) hours, the distance is 2 miles (which matches both graphs).
- At \( t = 2 \) hours, the distance is 7 miles (matches Option A).
- For larger time increments, Option A doesn’t provide further points, while Option B continues to increase but does not reflect the hiker's increasing distance after 2 hours.
Thus, the correct graph that shows how far the hiker will hike over time is **Option A**.
Given information:
- The hiker has already hiked 2 miles.
- The hiker walks at a pace of 5 miles every 2 hours.
From the pace, we can find the rate:
- 5 miles in 2 hours means the hiker walks at a rate of \( \frac{5 \text{ miles}}{2 \text{ hours}} = 2.5 \text{ miles per hour}\).
Now, let's analyze the hiker's distance over time starting from the 2 miles they've already completed.
At time \( t = 0 \) hours, the hiker has traveled 2 miles.
From this point on:
- After 1 hour: \( 2 \text{ miles} + (2.5 \text{ miles/hour} \times 1 \text{ hour}) = 2 + 2.5 = 4.5 \text{ miles} \)
- After 2 hours: \( 2 \text{ miles} + (2.5 \text{ miles/hour} \times 2 \text{ hours}) = 2 + 5 = 7 \text{ miles} \)
- After 4 hours: \( 2 \text{ miles} + (2.5 \text{ miles/hour} \times 4 \text{ hours}) = 2 + 10 = 12 \text{ miles} \)
- After 6 hours: \( 2 \text{ miles} + (2.5 \text{ miles/hour} \times 6 \text{ hours}) = 2 + 15 = 17 \text{ miles} \)
Now, we can look at the options:
**Option A** provides the points:
- (0, 2) and (2, 7)
**Option B** provides the points:
- (0, 5), (2, 10), (4, 15), and (6, 20)
Based on our calculations:
- At \( t = 0 \) hours, the distance is 2 miles (which matches both graphs).
- At \( t = 2 \) hours, the distance is 7 miles (matches Option A).
- For larger time increments, Option A doesn’t provide further points, while Option B continues to increase but does not reflect the hiker's increasing distance after 2 hours.
Thus, the correct graph that shows how far the hiker will hike over time is **Option A**.