A hiker starts climbing a hill from an elevation of $200~\text{feet}$ above sea level. After $20~\text{minutes}$, the hiker reaches an elevation of $800~\text{feet}$ above sea level. Let $h\left(t\right)$ represent the elevation (in feet) above sea level of the hiker $t$ minutes after starting the climb. Evaluate $\frac{h\left(20\right)-h\left(0\right)}{20-0}$ and select the correct interpretation of this quotient.

$30~\text{ft/min}$, The hiker climbs at an average rate of $30~\text{ft/min}$ during the last $20~\text{minutes}$ of the hike.

$6~\text{ft/min}$, The hiker climbs at an average rate of $6~\text{ft/min}$ during the first $20~\text{minutes}$ of the hike.

$30~\text{ft/min}$, The hiker climbs at an average rate of $30~\text{ft/min}$ during the first $20~\text{minutes}$ of the hike.

$20~\text{ft/min}$, The hiker climbs at an average rate of $20~\text{ft/min}$ during the first $20~\text{minutes}$ of the hike.