Question

1. grant walked 22 feet in 5 seconds, 66 feet in 15 seconds, and 264 feet in 60 seconds. use d to represent the distance in feet and t to represent the time in seconds.

Explanation:

Step1: Calculate speed for each case

For the first case, speed $v_1 = \frac{d_1}{t_1}=\frac{22}{5} = 4.4$ feet per second.
For the second case, $v_2=\frac{66}{15}=4.4$ feet per second.
For the third case, $v_3=\frac{264}{60} = 4.4$ feet per second.

Step2: Determine the relationship

Since the speed is constant ($4.4$ ft/s), the distance $d$ and time $t$ follow a direct - variation relationship. The formula for distance in terms of time (when speed is constant) is $d = vt$, where $v = 4.4=\frac{22}{5}$. So the equation is $d=\frac{22}{5}t$ or $d = 4.4t$.

Answer:

The relationship between distance \(d\) and time \(t\) is \(d=\frac{22}{5}t\) (or \(d = 4.4t\))