Question

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?

A) Emma travels 0.5 miles per hour faster than Becky.
B) Becky travels 0.5 miles per hour faster than Emma.
C) Emma travels 7 miles per hour faster than Becky.
D) Emma and Becky travel at the same speed.

Answer 1

B

Explanation:

Becky travels 0.5 miles per hour faster than Emma.

Emma's speed is 7.5 miles per hour. The slope of y = 8x, which is 8, is Becky's speed.

8 − 7.5 = 0.5 miles per hour faster

Answer 2

Option B. is the answer.

Explanation:

y = 8x is the function that represents the distance y miles traveled in x hours by Emma.

From the given function

Speed of Emma =
`(y)/(x)=8` miles per hour

Relation between distance covered (y) by Becky in (x) hours has been given in the table attached.

Then speed of Becky = Rate of change in distance traveled by Becky

Speed of Becky =
`((15-7.5))/((2-1))`

= 7.5 miles per hour

Difference in the speed of Becky and Emma = 8 - 7.5 = 0.5 miles per hour

That represents that Becky travels 0.5 miles per hour faster than Emma.

Option B). is the answer.