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

Answer:

Table 3

x | y

50 | 10

60 | 12

70 | 14

80 | 16

Step-by-step 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 = $\frac{7}{35} = \frac{1}{5}$.

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 = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 10}{55 - 50} = \frac{2}{5}$

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

Rate of change = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 10}{72 - 60} = \frac{2}{12} = \frac{1}{6}$

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

Rate of change = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 10}{60 - 50} = \frac{2}{10} = \frac{1}{5}$

This table has the same rate of change.

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

Rate of change = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 10}{84 - 70} = \frac{2}{14} = \frac{1}{7}$

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