Question

bike a and bike b are raced on a track. the following table shows the number of laps each completes in the same amount of time.
number of laps completed by bike a | number of laps completed by bike b
---|---
0.5 | 0.45
1.2 | 1.08
1.6 | 1.44

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

b. what is the constant of proportionality?

c. when bike a completes 70 laps, how many laps does bike b complete in the same amount of time?

d. if bike a completes 100 laps, how many does bike b complete in the same amount of time?

Explanation:

Step1: Analyze relationship type

Check ratio consistency:
$\frac{0.45}{0.5}=0.9$, $\frac{1.08}{1.2}=0.9$, $\frac{1.44}{1.6}=0.9$

Step2: Identify constant of proportionality

The constant is the consistent ratio:
$\text{Constant} = \frac{\text{Laps of Bike B}}{\text{Laps of Bike A}} = 0.9$

Step3: Calculate laps for Bike B (70 laps A)

Multiply A's laps by constant:
$70 \times 0.9 = 63$

Step4: Calculate laps for Bike B (100 laps A)

Multiply A's laps by constant:
$100 \times 0.9 = 90$

Answer:

a. The data shows a proportional (direct linear) relationship. The ratio of laps completed by Bike B to Bike A is constant (0.9) for all data pairs.
b. $0.9$
c. $63$
d. $90$