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.