Question
Your neighbor burns 121 Calories in 11 minutes cross-country skiing. There is a proportional relationship between Calories burned and time. Find the unit rate. Then use the unit rate to graph this relationship.
Question content area bottom
Part 1
The unit rate is
enter your response here Calories per minute.
Part 2
Which graph represents the relationship between time and Calories burned?
A.
Skiing
0
3
0
99
Time (minutes)
Calories Burned
A coordinate plane is titled Skiing. A horizontal axis is labeled Time (minutes) from 0 to 3. A vertical axis is labeled Calories Burned from 0 to 99. A curve rises from the origin, (0, 0), at an increasing rate and passes through the points (1, 11) and (2, 44).
B.
Skiing
0
3
0
44
Calories Burned
Time (minutes)
A coordinate plane is titled Skiing. A horizontal axis is labeled Time (minutes) from 0 to 3. A vertical axis is labeled Calories Burned from 0 to 44. A line rises from left to right and passes through the points (0, 11) and (1, 22).
C.
Skiing
0
3
0
33
Time (minutes)
Calories Burned
Question content area bottom
Part 1
The unit rate is
enter your response here Calories per minute.
Part 2
Which graph represents the relationship between time and Calories burned?
A.
Skiing
0
3
0
99
Time (minutes)
Calories Burned
A coordinate plane is titled Skiing. A horizontal axis is labeled Time (minutes) from 0 to 3. A vertical axis is labeled Calories Burned from 0 to 99. A curve rises from the origin, (0, 0), at an increasing rate and passes through the points (1, 11) and (2, 44).
B.
Skiing
0
3
0
44
Calories Burned
Time (minutes)
A coordinate plane is titled Skiing. A horizontal axis is labeled Time (minutes) from 0 to 3. A vertical axis is labeled Calories Burned from 0 to 44. A line rises from left to right and passes through the points (0, 11) and (1, 22).
C.
Skiing
0
3
0
33
Time (minutes)
Calories Burned
Answers
GPT-4o mini
To find the unit rate of Calories burned per minute while cross-country skiing, you can divide the total Calories burned by the total time taken.
Given:
- Total Calories burned = 121 Calories
- Total time = 11 minutes
**Unit Rate Calculation:**
\[
\text{Unit Rate} = \frac{\text{Total Calories}}{\text{Total Time}} = \frac{121 \text{ Calories}}{11 \text{ minutes}} = 11 \text{ Calories per minute}
\]
So, the unit rate is **11 Calories per minute**.
### Part 2: Graphing the Relationship
Since the relationship is proportional (directly related), the graph should be a straight line starting from the origin (0, 0), where each minute corresponds to an increase of 11 Calories.
Now we calculate Calories burned for specific time intervals:
1. At 1 minute: \(1 \times 11 = 11\) Calories
2. At 2 minutes: \(2 \times 11 = 22\) Calories
3. At 3 minutes: \(3 \times 11 = 33\) Calories
Given the provided options:
**A.** The graph represents an increasing curve, which does not correspond to a proportional relationship.
**B.** The graph shows a line that passes through the points (0, 11) and (1, 22), which does not start at the origin. Therefore, it also does not represent the proportional relationship correctly.
**C.** The graph represents a straight line that starts from the origin and rises, but it includes points that don’t correctly represent the relationship (it should go through (0, 0), (1, 11), (2, 22), and (3, 33)).
None of the available graphs directly represent the accurate linear relationship based on the derived unit rate of 11 Calories per minute.
However, you can plot the points based on our calculations:
- (0, 0)
- (1, 11)
- (2, 22)
- (3, 33)
If you have the option to suggest a new graph, that would be the correct representation of the relationship between time and Calories burned based on the calculated unit rate of **11 Calories per minute**.
Given:
- Total Calories burned = 121 Calories
- Total time = 11 minutes
**Unit Rate Calculation:**
\[
\text{Unit Rate} = \frac{\text{Total Calories}}{\text{Total Time}} = \frac{121 \text{ Calories}}{11 \text{ minutes}} = 11 \text{ Calories per minute}
\]
So, the unit rate is **11 Calories per minute**.
### Part 2: Graphing the Relationship
Since the relationship is proportional (directly related), the graph should be a straight line starting from the origin (0, 0), where each minute corresponds to an increase of 11 Calories.
Now we calculate Calories burned for specific time intervals:
1. At 1 minute: \(1 \times 11 = 11\) Calories
2. At 2 minutes: \(2 \times 11 = 22\) Calories
3. At 3 minutes: \(3 \times 11 = 33\) Calories
Given the provided options:
**A.** The graph represents an increasing curve, which does not correspond to a proportional relationship.
**B.** The graph shows a line that passes through the points (0, 11) and (1, 22), which does not start at the origin. Therefore, it also does not represent the proportional relationship correctly.
**C.** The graph represents a straight line that starts from the origin and rises, but it includes points that don’t correctly represent the relationship (it should go through (0, 0), (1, 11), (2, 22), and (3, 33)).
None of the available graphs directly represent the accurate linear relationship based on the derived unit rate of 11 Calories per minute.
However, you can plot the points based on our calculations:
- (0, 0)
- (1, 11)
- (2, 22)
- (3, 33)
If you have the option to suggest a new graph, that would be the correct representation of the relationship between time and Calories burned based on the calculated unit rate of **11 Calories per minute**.