Question

1. bike a and bike b are raced on a trail. the following table shows the number of laps of the trail that are completed by each bike in the same amount of time.

number of laps completed by bike a	number of laps completed by bike b
0.8	1.44
1.5	2.7

a. which bike has a faster speed? explain.

b. what type of relationship do the data values display? why?

c. what is the constant of proportionality?

d. if bike a completes 20 laps, how many laps does bike b complete in the same amount of time?

Explanation:

Step1: Calculate Bike B/Bike A ratio

$\frac{0.54}{0.3}=1.8$, $\frac{1.44}{0.8}=1.8$, $\frac{2.7}{1.5}=1.8$

Step2: Compare speeds (laps per time)

Bike B completes 1.8x laps of Bike A.

Step3: Identify relationship type

Ratio of laps is constant (1.8).

Step4: Define constant of proportionality

It's the fixed ratio of Bike B to Bike A laps.

Step5: Calculate laps for Bike B at 20 A laps

$20 \times 1.8 = 36$

Answer:

a. Bike B has a faster speed. In the same amount of time, Bike B always completes 1.8 times as many laps as Bike A, meaning it covers more distance (laps) in the same time period.
b. The data shows a proportional (direct variation) relationship. The ratio of the number of laps completed by Bike B to Bike A is a constant 1.8 for all data pairs, which is the defining feature of a proportional relationship.
c. 1.8
d. 36