Question

Drew and Duck participated in a $4$ miles road race. Which statement is incorrect?

Answer 1

Lets see each option and then compare it with graphs given for Drew and Duck’s race.



$\bullet$ Drew and Duck completed the race at point $(40,4)$ and $(35,4)$, respectively.
$\bullet$ This means that Drew covered $4$ miles in $40$ minutes, and Duck covered 4 miles in $35$ minutes.
$\bullet$ This tells us that both covered the same distance, i.e., $4$ miles.
$\bullet$ This also tells us that Duck took $5$ minutes $(40-35)$ less to complete the same distance as that of Drew.
$\bullet$ Hence, Duck won the race by $5$ minutes.

Therefore, Option A and Option B are true for the graph.

Option C: Drew’s speed is linear between $20$ to $40$ minutes.


$\bullet$ The line segments from $20$ minutes and $40$ minutes pass through the point $(20,2)$ and $(40,4)$.
$\bullet$ The graph is a straight line between the given intervals.
Hence, it is a linear function.

Therefore, Drew's speed is linear between $20$ and $40$ minutes.
Hence, Option C is true.

Option D: Duck’s graph shows a linear function throughout.


We know that, in a graph, when the rate of change or slope is the same and the graph is a straight line, then it is a linear function
$\bullet$ Here, in Duck’s graph we could see that the graph is not a straight line throughout the race. Hence, it is not a linear function.

Therefore, Option D is not true.

$\to$ Option D is correct.