Question

Distance (miles) Time (hours)
7.5 1
15 2
22.5 3
30 4


The table represents the distance covered by Emma over several hours on a recent Saturday bike ride. Becky takes the same route, and the total distance she travels, y miles, in x hours is represented by the function y = 8x. Assuming that Emma and Becky travel at a constant rate of speed, which statement BEST compares their biking speeds?
Responses
A Emma travels 0.5 miles per hour faster than Becky.Emma travels 0.5 miles per hour faster than Becky.
B Becky travels 0.5 miles per hour faster than Emma.Becky travels 0.5 miles per hour faster than Emma.
C Emma travels 7 miles per hour faster than Becky.Emma travels 7 miles per hour faster than Becky.
D Emma and Becky travel at the same speed.

Answer 1

To compare the biking speeds of Emma and Becky, we first need to determine their speeds from the information provided.

**Emma's Speeds:**
We can calculate Emma's speed from the data in the table by finding the distance covered per hour.

- From the table, Emma's distance and time values are:
- \(7.5\) miles in \(1\) hour
- \(15\) miles in \(2\) hours
- \(22.5\) miles in \(3\) hours
- \(30\) miles in \(4\) hours

Emma's speed is consistent, and we can find it by using any of these values:
- Speed = Distance / Time

Using \(7.5\) miles in \(1\) hour:
- Emma's speed = \( \frac{7.5 \text{ miles}}{1 \text{ hour}} = 7.5 \text{ miles per hour} \)

**Becky's Speed:**
The function provided for Becky is \(y = 8x\). This indicates that Becky travels \(8\) miles in \(1\) hour.

Thus, Becky's speed is:
- Speed = \(8\) miles per hour.

**Comparison:**
- Emma's speed = \(7.5\) miles per hour
- Becky's speed = \(8\) miles per hour

Now we can compare their speeds:
- Becky's speed \(8\) miles per hour is greater than Emma's speed \(7.5\) miles per hour by \(8 - 7.5 = 0.5\) miles per hour.

Thus, the correct statement is:
**B. Becky travels 0.5 miles per hour faster than Emma.**