Question

3. A rabbit and turtle are in a race. Is the relationship between distance

traveled and time proportional for either one? If so, write an equation that

represents the relationship.

Turtle's Run:

1

Distance (meters)

108 Comp

405 0.145

540 16

1,768.5

Time (minutes)

2

7.5

Rabbit's Run:

Distance (meters) Time (minutes)

800 900

900 0.bas

1,107.

50

1,524 ,211 32.5

10

20

32.75

Answer 1

The relationship is proportional for the turtle and the equation is Distance = 54*Time

Explanation:

Turtle’s run:

Distance (meters) | Time (minutes)

108 | 2

405 | 7.5

540 | 10

1768.5 | 32.75

Rabbitt’s run:

Distance (meters) | Time (minutes)

800 | 1

900 | 5

1107.5 | 20

1524 | 32.5

The relationship between distance traveled and time is proportional if this equation is satisfied:

Distance = k*Time or k = Distance/Time

where k is a constant

For the turtle:

108/2 = 405/7.5 = 540/10 = 1768.5/32.75 = 54

Then, the relationship is proportional and the equation is Distance = 54*Time

For the rabbit:

800/ 1 = 800

900/5 = 180

1107.5/20 = 55.375

1524/32.5 = 46.89

Then, the relationship is not proportional.