Question

A bike is travelling at a constant speed. After 35 minutes, it travels 7 miles. Which table represents the relationship between the time in minutes, x, and the distance the bike travles, y?

Answer 1

Table 3

x | y

50 | 10

60 | 12

70 | 14

80 | 16

Explanation:

x = time in minutes

y = distance travelled

Given that the bike travelled 7 miles after 35 minutes at a constant speed, the rate of change =
`(7)/(35) = (1)/(5)`.

Thus, the table that represents the relationship between the time in minutes, x, and the distance the bike travles, y would have the same rate of change of ⅕.

Calculate the rate of change of each table using any two given pairs on the table:

Table 1: using (50, 10) and (55, 12)

Rate of change =
`(y_2 - y_1)/(x_2 - x_1) = (12 - 10)/(55 - 50) = (2)/(5)`

Table 2: using (60, 10) and (72, 12)

Rate of change =
`(y_2 - y_1)/(x_2 - x_1) = (12 - 10)/(72 - 60) = (2)/(12) = (1)/(6)`

Table 3: using (50, 10) and (60, 12)

Rate of change =
`(y_2 - y_1)/(x_2 - x_1) = (12 - 10)/(60 - 50) = (2)/(10) = (1)/(5)`

This table has the same rate of change.

Table 4: using (70, 10) and (84, 12)

Rate of change =
`(y_2 - y_1)/(x_2 - x_1) = (12 - 10)/(84 - 70) = (2)/(14) = (1)/(7)`

Table 3 represents the relationship between the time in minutes, x, and the distance the bike travles, y.