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 runs 6 yards per second. nancy is new to the team, so she starts 10 yards ahead of the starting line. initial value for paula’s function: 0 initial value for nancy’s function: 10 paula’s rate of change: 7 nancy’s rate of change: 6 compare the speeds of the runners. the rate of change for paula is? the rate of change for nancy: that means? runs at a faster speed. paula: time (seconds), x distance (yards), y 0 0 10 70 20 140

Explanation:

Step1: Calculate Paula's rate of change

To find the rate of change (speed) for Paula, we use the formula for slope (rate of change) which is $\frac{\Delta y}{\Delta x}$. Using two points from her table, say $(0, 0)$ and $(10, 70)$, the change in $y$ is $70 - 0 = 70$ and change in $x$ is $10 - 0 = 10$. So rate of change is $\frac{70}{10} = 7$.

Step2: Compare rates of change

Paula's rate of change is 7 (yards per second) and Nancy's rate of change is 6 (yards per second). Since $7>6$, Paula's rate of change is greater than Nancy's. So the rate of change for Paula is greater than the rate of change for Nancy. That means Paula runs at a faster speed.

Answer:

greater than the rate of change for Nancy; Paula