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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

They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.

object C
object C

object A
object A

object B
object B
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1 answer

To determine which object would reach 100 feet in the least amount of time, we need to analyze the lines on the graph based on their slopes.

  1. Line A passes through (0, 0) and (3, 6). The slope of line A is: \[ \text{slope of A} = \frac{6 - 0}{3 - 0} = 2 \text{ feet per second} \]

  2. Line B passes through (0, 0) and (6, 6). The slope of line B is: \[ \text{slope of B} = \frac{6 - 0}{6 - 0} = 1 \text{ foot per second} \]

  3. Line C passes through (0, 0) and (6, 3). The slope of line C is: \[ \text{slope of C} = \frac{3 - 0}{6 - 0} = 0.5 \text{ feet per second} \]

Now, we can calculate the time it takes for each object to reach 100 feet:

  • Object A: \[ \text{Time} = \frac{100 \text{ feet}}{2 \text{ feet/second}} = 50 \text{ seconds} \]

  • Object B: \[ \text{Time} = \frac{100 \text{ feet}}{1 \text{ foot/second}} = 100 \text{ seconds} \]

  • Object C: \[ \text{Time} = \frac{100 \text{ feet}}{0.5 \text{ feet/second}} = 200 \text{ seconds} \]

From this analysis, object A reaches 100 feet in the least amount of time (50 seconds).

Therefore, the correct answer is:

object A