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 B
object B
object C
object C
object A
object A
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 B
object B
object C
object C
object A
object A
They would all reach 100 feet at the same time.
Answers
GPT-4o mini
To determine which object would reach 100 feet in the least amount of time based on the provided lines and coordinates, we need to analyze the slopes of each line. The slope of a line in a distance-time graph represents the speed; a steeper slope means a greater speed.
1. **Line A** passes through the points (0, 0) and (3, 6).
- The slope is calculated as (change in distance)/(change in time) = (6 - 0)/(3 - 0) = 6/3 = 2 feet/second.
2. **Line B** passes through the points (0, 0) and (6, 6).
- The slope is (6 - 0)/(6 - 0) = 6/6 = 1 foot/second.
3. **Line C** passes through the points (0, 0) and (6, 3).
- The slope is (3 - 0)/(6 - 0) = 3/6 = 0.5 feet/second.
Now, we can find the time it would take each object to reach 100 feet using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
- For **Line A**:
\[
\text{Time} = \frac{100 \text{ feet}}{2 \text{ feet/second}} = 50 \text{ seconds}
\]
- For **Line B**:
\[
\text{Time} = \frac{100 \text{ feet}}{1 \text{ foot/second}} = 100 \text{ seconds}
\]
- For **Line C**:
\[
\text{Time} = \frac{100 \text{ feet}}{0.5 \text{ feet/second}} = 200 \text{ seconds}
\]
From this analysis, the object represented by **Line A** reaches 100 feet in the least amount of time, which is 50 seconds.
**Final answer: object A**.
1. **Line A** passes through the points (0, 0) and (3, 6).
- The slope is calculated as (change in distance)/(change in time) = (6 - 0)/(3 - 0) = 6/3 = 2 feet/second.
2. **Line B** passes through the points (0, 0) and (6, 6).
- The slope is (6 - 0)/(6 - 0) = 6/6 = 1 foot/second.
3. **Line C** passes through the points (0, 0) and (6, 3).
- The slope is (3 - 0)/(6 - 0) = 3/6 = 0.5 feet/second.
Now, we can find the time it would take each object to reach 100 feet using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
- For **Line A**:
\[
\text{Time} = \frac{100 \text{ feet}}{2 \text{ feet/second}} = 50 \text{ seconds}
\]
- For **Line B**:
\[
\text{Time} = \frac{100 \text{ feet}}{1 \text{ foot/second}} = 100 \text{ seconds}
\]
- For **Line C**:
\[
\text{Time} = \frac{100 \text{ feet}}{0.5 \text{ feet/second}} = 200 \text{ seconds}
\]
From this analysis, the object represented by **Line A** reaches 100 feet in the least amount of time, which is 50 seconds.
**Final answer: object A**.