Question

mel slides down waterslide a, and victor slides down waterslide b. after 2 seconds, mel was 50 feet in the air, and after 5 seconds, she was 35 feet in the air. after 1 second, victor was 60 feet in the air, and after 4 seconds, he was 50 feet in the air. who was descending at a faster rate? mel: (2, 50) and (5, 35) victor: (1, 60) and (4, 50) mels rate of change is. that means that her height in the air decreases feet every second. victors rate of change is. that means that his height in the air decreases feet every second.

Explanation:

Step1: Calculate Mel's rate of change

The rate - of - change formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For Mel, $(x_1,y_1)=(2,50)$ and $(x_2,y_2)=(5,35)$. So $m_{Mel}=\frac{35 - 50}{5 - 2}=\frac{- 15}{3}=-5$.

Step2: Calculate Victor's rate of change

For Victor, $(x_1,y_1)=(1,60)$ and $(x_2,y_2)=(4,50)$. So $m_{Victor}=\frac{50 - 60}{4 - 1}=\frac{-10}{3}\approx - 3.33$.

Step3: Compare the rates of change

The absolute value of Mel's rate of change $|m_{Mel}| = 5$, and the absolute value of Victor's rate of change $|m_{Victor}|=\frac{10}{3}\approx3.33$. Since $5>\frac{10}{3}$, Mel is descending at a faster rate.

Answer:

Mel's rate of change is - 5. That means that her height in the air decreases 5 feet every second.
Victor's rate of change is $-\frac{10}{3}$. That means that his height in the air decreases $\frac{10}{3}\approx3.33$ feet every second. Mel is descending at a faster rate.