Question

Use the data in the table to identify the speed of a moving object, Object A.
x y
4 1
8 2
12 3
16 4

Use the y = 1/5 x to identify the speed of another moving object, Object B.

Compare the speeds of Object A and Object B. Which of the two moving objects has greater speed and by what factor? (round to nearest hundredth)

Hint: The factor is equivalent to the ratio of the faster speed to the slower speed.


A Object A is moving faster by a factor of 1.05Object A is moving faster by a factor of 1.05
B Object B is moving faster by a factor of 1.05Object B is moving faster by a factor of 1.05
C Object A is moving faster by a factor of 1.25Object A is moving faster by a factor of 1.25
D Object B is moving faster by a factor of 1.25

Answer 1

To determine the speeds of both Object A and Object B, we can analyze the data provided for Object A and the equation for Object B.

### Object A:
We have the following data points for Object A:

| x | y |
|---|---|
| 4 | 1 |
| 8 | 2 |
| 12 | 3 |
| 16 | 4 |

The relationship between x and y shows a linear pattern. We can find the speed (or rate of change) by looking at the change in y values over the change in x values:

1. From (4, 1) to (8, 2):
- Δy = 2 - 1 = 1
- Δx = 8 - 4 = 4
- Speed = Δy / Δx = 1 / 4 = 0.25

2. From (8, 2) to (12, 3):
- Δy = 3 - 2 = 1
- Δx = 12 - 8 = 4
- Speed = 1 / 4 = 0.25

3. From (12, 3) to (16, 4):
- Δy = 4 - 3 = 1
- Δx = 16 - 12 = 4
- Speed = 1 / 4 = 0.25

The speed for Object A is consistently 0.25.

### Object B:
The equation given for Object B is:
\[ y = \frac{1}{5} x \]

To find the speed of Object B, we can deduce it from the slope of the equation:
- The equation shows that for every increase of 5 in x, y increases by 1.
- Thus, the speed (rate of change of y with respect to x) is \( \frac{1}{5} = 0.2 \).

### Comparison of Speeds:
- Speed of Object A = 0.25
- Speed of Object B = 0.2

Now, we can compare the two speeds:
- Since 0.25 is greater than 0.2, Object A is faster.

To find the factor by which Object A is faster than Object B:
\[ \text{Factor} = \frac{\text{Speed of Object A}}{\text{Speed of Object B}} = \frac{0.25}{0.2} = 1.25 \]

### Conclusion:
The faster object is Object A compared to Object B, and the factor by which Object A is faster is **1.25**.

Thus, the correct option is:
**C: Object A is moving faster by a factor of 1.25.**