Question

part 1 of 2
error analysis a question on a test asks students to find the speed at which a car travels. the graph shows a proportional relationship between the distance traveled in miles and time in hours.
anna incorrectly says that the speed of the car is \\(\frac{1}{55}\\) mile per hour. what is the speed of the car?
what error might anna have made?

the speed of the car is \\(\square\\) miles per hour.

(graph: speed of a car, x-axis: time (hours) from 0 to 5, y-axis: distance (miles) from 0 to 275, with a line passing through (0,0), (1,55), (2,110), (3,165), (4,220), (5,275))

Explanation:

Step1: Recall speed formula

Speed is calculated as \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \). For a proportional relationship, we can use any point \((t, d)\) on the graph where \(d\) is distance and \(t\) is time.

Step2: Choose a point from the graph

Looking at the graph, when \( t = 1 \) hour, the distance \( d = 55 \) miles (or we can use another point, like \( t = 2 \), \( d = 110 \); the ratio will be the same).

Step3: Calculate speed

Using the formula \( \text{Speed} = \frac{d}{t} \), substitute \( d = 55 \) miles and \( t = 1 \) hour. So \( \text{Speed} = \frac{55}{1} = 55 \) miles per hour.

To find the error Anna made: She likely inverted the ratio, using \( \frac{\text{Time}}{\text{Distance}} \) instead of \( \frac{\text{Distance}}{\text{Time}} \). For example, if she took \( t = 1 \) and \( d = 55 \), she calculated \( \frac{1}{55} \) instead of \( \frac{55}{1} \).

Answer:

The speed of the car is \( \boldsymbol{55} \) miles per hour.