Question

paula and nancy race at track practice. paula records her time in a table where her distance in yards, y, is a function of her time in seconds, x. nancy is new to the team, so she starts 10 yards ahead of the starting line. nancy runs 6 yards per second.
initial value for paula’s function: 0
initial value for nancy’s function: 10
what is paula’s speed? find the rate of change.
paula’s speed =
yards per second
paula:
time (seconds), x | distance (yards), y
0 | 0
10 | 70
20 | 140

Explanation:

Step1: Identify the formula for speed

Speed is calculated as the rate of change of distance with respect to time, which is given by the formula \( \text{speed} = \frac{\text{change in distance}}{\text{change in time}} \).

Step2: Calculate the change in distance and time for Paula

From the table, at \( x = 0 \) (time = 0 seconds), \( y = 0 \) yards. At \( x = 10 \) seconds, \( y = 70 \) yards. The change in distance \( \Delta y = 70 - 0 = 70 \) yards, and the change in time \( \Delta x = 10 - 0 = 10 \) seconds.

Step3: Compute Paula's speed

Using the speed formula, \( \text{speed} = \frac{70}{10} = 7 \) yards per second.

Answer:

7