A park ranger needs to quickly get from their current location to a lost hiker who is 30 m 30\text{ m} 30 m away from a landmark tree, which is 30 m 30\text{ m} 30 m directly east of the ranger. The ranger can jog at a speed of 6 m/s 6\text{ m/s} 6 m/s on the trail and hike through the woods at a speed of 2 m/s 2\text{ m/s} 2 m/s . Determine the travel time function T ( x ) T(x) T ( x ) , where 0 ≤ x ≤ 30 0\le x\le30 .

T = 30 − x 6 + x 2 + 900 2 T=\frac{30 - x}{6}+\frac{\sqrt{x^2+900}}{2}

T = 30 − x 2 + x 2 + 30 6 T=\frac{30-x}{2}+\frac{\sqrt{x^2+30}}{6}

T = 30 − x 2 + x 2 + 900 6 T=\frac{30-x}{2}+\frac{\sqrt{x^2+900}}{6}

T = 30 − x 6 + x 2 + 30 2 T=\frac{30 - x}{6}+\frac{\sqrt{x^2+30}}{2}

A park ranger needs to quickly get from their current location to...

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