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 = 7 yards per second
what is nancy’s speed? find the rate of change.
nancy’s speed = \boxed{} yards per second
paula:

time (seconds), x	0	10	20
distance (yards), y	0	70	140

Explanation:

Step1: Recall the formula for speed (rate of change)

Speed \(=\frac{\text{Change in distance}}{\text{Change in time}}\)

Step2: Identify the values for Nancy

Nancy's speed is given in the problem description. She runs at a constant rate. The formula for her distance \(y\) as a function of time \(x\) is \(y = 6x+ 10\) (where the slope \(m\) in the linear function \(y=mx + b\) represents the speed). The coefficient of \(x\) in a linear function \(y = mx + b\) (where \(y\) is distance and \(x\) is time) is the rate of change (speed).

Answer:

6