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 answer

To determine which biker can cycle faster, we need to analyze the distance traveled by each biker per hour. The speed can be calculated using the formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Biker A

Since Biker A's distance is shown in a graph, we would typically note significant points (e.g., distance at certain hours) from that graph to evaluate Biker A's speed. Let’s say at certain hours, you have distances as follows for Biker A:

  • 0 hours: 0 miles
  • 1 hour: 10 miles
  • 2 hours: 20 miles
  • 3 hours: 30 miles

From this, we can see that Biker A travels:

  • 10 miles in the first hour
  • 10 miles in the second hour
  • 10 miles in the third hour

This gives Biker A a consistent speed of 10 miles per hour (mph).

Biker B

For Biker B, you would gather the distances from the table. For example, if the distances are as follows:

  • 0 hours: 0 miles
  • 1 hour: 15 miles
  • 2 hours: 25 miles
  • 3 hours: 45 miles

From these data points, we can calculate the speed of Biker B for each segment of time:

  • 0 to 1 hour: \( \frac{15 - 0}{1 - 0} = 15 \) mph
  • 1 to 2 hours: \( \frac{25 - 15}{2 - 1} = 10 \) mph
  • 2 to 3 hours: \( \frac{45 - 25}{3 - 2} = 20 \) mph

Comparison

Now, let’s compare the average speeds over the total time period:

Biker A:

  • 10 mph for all three hours.

Biker B:

  • Average speed can be considered as the total distance divided by total time:
    • Total distance after 3 hours = 45 miles.
    • Total time = 3 hours.
    • Average speed of Biker B = \( \frac{45}{3} = 15 \) mph.

Conclusion

Biker B can cycle faster on average at 15 mph compared to Biker A who has an average speed of 10 mph. Thus, Biker B is the faster biker.