Question
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these objects would reach 100 feet in the least amount of time?
(1 point)
Responses
object A
object A
object B
object B
object C
object C
They would all reach 100 feet at the same time.
Which of these objects would reach 100 feet in the least amount of time?
(1 point)
Responses
object A
object A
object B
object B
object C
object C
They would all reach 100 feet at the same time.
Answers
GPT-4o mini
To determine which object reaches 100 feet in the least amount of time, we can analyze the slopes of each line:
1. **Line A** passes through (0, 0) and (3, 6):
- The slope (representing speed) can be calculated as change in distance divided by change in time:
\[
\text{slope of A} = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \text{ feet/second}
\]
2. **Line B** passes through (0, 0) and (6, 6):
- The slope is:
\[
\text{slope of B} = \frac{6 - 0}{6 - 0} = \frac{6}{6} = 1 \text{ foot/second}
\]
3. **Line C** passes through (0, 0) and (6, 3):
- The slope is:
\[
\text{slope of C} = \frac{3 - 0}{6 - 0} = \frac{3}{6} = 0.5 \text{ feet/second}
\]
Now, to find the time taken to reach 100 feet for each object, we can use the formula:
\[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
- For **Line A**:
\[
\text{time for A} = \frac{100 \text{ feet}}{2 \text{ feet/second}} = 50 \text{ seconds}
\]
- For **Line B**:
\[
\text{time for B} = \frac{100 \text{ feet}}{1 \text{ foot/second}} = 100 \text{ seconds}
\]
- For **Line C**:
\[
\text{time for C} = \frac{100 \text{ feet}}{0.5 \text{ feet/second}} = 200 \text{ seconds}
\]
Based on this analysis, object A would reach 100 feet in the least amount of time, which is 50 seconds.
**Response**: object A
1. **Line A** passes through (0, 0) and (3, 6):
- The slope (representing speed) can be calculated as change in distance divided by change in time:
\[
\text{slope of A} = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \text{ feet/second}
\]
2. **Line B** passes through (0, 0) and (6, 6):
- The slope is:
\[
\text{slope of B} = \frac{6 - 0}{6 - 0} = \frac{6}{6} = 1 \text{ foot/second}
\]
3. **Line C** passes through (0, 0) and (6, 3):
- The slope is:
\[
\text{slope of C} = \frac{3 - 0}{6 - 0} = \frac{3}{6} = 0.5 \text{ feet/second}
\]
Now, to find the time taken to reach 100 feet for each object, we can use the formula:
\[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
- For **Line A**:
\[
\text{time for A} = \frac{100 \text{ feet}}{2 \text{ feet/second}} = 50 \text{ seconds}
\]
- For **Line B**:
\[
\text{time for B} = \frac{100 \text{ feet}}{1 \text{ foot/second}} = 100 \text{ seconds}
\]
- For **Line C**:
\[
\text{time for C} = \frac{100 \text{ feet}}{0.5 \text{ feet/second}} = 200 \text{ seconds}
\]
Based on this analysis, object A would reach 100 feet in the least amount of time, which is 50 seconds.
**Response**: object A