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A line graph is titled as “Biker A’s Distance Traveled”. The x-axis is labeled “Hours spent biking”, ranging from 0 to 4, in increments of 1. The y-axis is labeled “Miles Traveled”. A solid line joins four plotted points. The coordinates of the plotted points are as follows: (0, 0), (1, 15), (2, 30), (3, 45).

This table shows the number of miles Biker B traveled based on the hours spent biking.
strong>Biker B's Distance Traveled Per Hour
Hours spent biking Miles Traveled
1 12
2 24
3 36
Two bikers track how many miles they traveled for each hour they spent biking. Biker A's distance traveled is shown in the graph above. Biker B's distance traveled is shown in the table above. Using the data above, which Biker can cycle faster? How fast were they traveling?


(1 point)
Responses

Biker B can cycle faster, 12 mph
Biker B can cycle faster, 12 mph

Biker A can cycle faster, 15 mph
Biker A can cycle faster, 15 mph

Biker A can cycle faster, 12 mph
Biker A can cycle faster, 12 mph

Biker B can cycle faster, 15 mph

1 answer

To determine which biker cycles faster, we need to calculate their speeds in miles per hour (mph).

Biker A

From the graph:

  • Biker A travels 15 miles in 1 hour, 30 miles in 2 hours, and 45 miles in 3 hours.

To find the speed:

  • Speed for Biker A: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)

For Biker A:

  • At 1 hour: \( \frac{15 \text{ miles}}{1 \text{ hour}} = 15 \text{ mph} \)
  • At 2 hours: \( \frac{30 \text{ miles}}{2 \text{ hours}} = 15 \text{ mph} \)
  • At 3 hours: \( \frac{45 \text{ miles}}{3 \text{ hours}} = 15 \text{ mph} \)

Biker A travels at a consistent speed of 15 mph.

Biker B

From the table:

  • Biker B travels 12 miles in 1 hour, 24 miles in 2 hours, and 36 miles in 3 hours.

For Biker B:

  • At 1 hour: \( \frac{12 \text{ miles}}{1 \text{ hour}} = 12 \text{ mph} \)
  • At 2 hours: \( \frac{24 \text{ miles}}{2 \text{ hours}} = 12 \text{ mph} \)
  • At 3 hours: \( \frac{36 \text{ miles}}{3 \text{ hours}} = 12 \text{ mph} \)

Biker B travels at a consistent speed of 12 mph.

Conclusion

Comparing the speeds:

  • Biker A: 15 mph
  • Biker B: 12 mph

Therefore, Biker A can cycle faster at 15 mph.

The correct response is: Biker A can cycle faster, 15 mph.