Answer
$(a)$
At first Miyuki swims to the pool edge and returns back in the same time. Then again swims to the edge of the pool and returns back. And at last again swiems to the edge and stops.
The average rate of change is $\frac{5}{3}m/s$
$(b)$ See the image below.
We have the new graph by stretching the old one by the factor of $1.2$. Multyplying $y$ values by $1.2$ times.
$(c)$ The new speed is $2m/s$
Work Step by Step
$(a)$
At first Miyuki swims to the pool edge and returns back in the same time. Then again swims to the edge of the pool and returns back. And at last again swiems to the edge and stops.
The average rate of change is $\frac{Δ y}{Δ x} = \frac{50}{30}=\frac{5}{3}m/s$
Note, the average speed is the same as $m$ slope.
$(b)$ See the image above.
We have the new graph by stretching the old one by the factor of $1.2$. Multyplying $y$ values by $1.2$ times.
$(c)$ The new speed is :
$\frac{60}{30}=2m/s$
In this case the first distance $50$ is multiplied by $1.2$ which equals to $60$.
