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 average rate? Write ordered pairs relating Mel's and Victor's positions at a given time (i.e . (time, height)) Mel: (2,square ) ) and (5, (5,square ) DONE Victor: (1, (1,square ) and square square DONE

## Step 1<br />The problem involves the concept of average rate of change, which is a measure of how a quantity changes over time. In this case, we are given the positions of Mel and Victor at different times and asked to determine who is descending at a faster average rate.<br /><br />## Step 2<br />To find the average rate of change, we need to calculate the slope of the line that connects the two points for each person. The slope is calculated by the formula:<br /><br />### \(m = \frac{y_2 - y_1}{x_2 - x_1}\)<br /><br />where \(m\) is the slope, \(x_1\) and \(x_2\) are the x-coordinates of the two points, and \(y_1\) and \(y_2\) are the y-coordinates of the two points.<br /><br />## Step 3<br />For Mel, the points are (2, 50) and (5, 35). Substituting these values into the slope formula gives:<br /><br />### \(m_{Mel} = \frac{35 - 50}{5 - 2} = -5\)<br /><br />This means that Mel is descending at an average rate of 5 feet per second.<br /><br />## Step 4<br />For Victor, the points are (1, 60) and (4, 50). Substituting these values into the slope formula gives:<br /><br />### \(m_{Victor} = \frac{50 - 60}{4 - 1} = -6.67\)<br /><br />This means that Victor is descending at an average rate of 6.67 feet per second.<br /><br />## Step 5<br />Comparing the two rates, we can see that Victor is descending at a faster average rate than Mel.