Q:

Jamie is hiking up a small mountain. He climbs up at a constant rate of 300 feet/hour until he reaches the peak at 1,500 feet. After that, he hikes down at the same rate to the base of the mountain. The equation that models Jamie's elevation, e, after t hours is e = . Jamie's elevation will be 600 feet after hours and after hours.

Accepted Solution

A:
Answer:1). 300 = {Δx}{Δt} 2). 2 hours and 3 hoursStep-by-step explanation:Let Jamie reaches at height 1500 feet after t hours and after time t' Jamie is at the height x feet.Therefore, equation that represents elevation of Jamie will be⇒ Rate of change in elevation e = $$\frac{\text{Change in height}}{\text{Change in time}}$$e = (Δx)/Δt 300 = $$\frac{x-0}{t-0}$$ [While hiking up from x = 0 and t = 0]300 = $$\frac{1500-x}{t-t'}$$ [ While hiking down from x = 1500 and t = 0]1). If Jamie's elevation is 600 feet while hiking down.Then $$300=\frac{1500-600}{\text{Change in time}}$$Change in time = $$\frac{900}{300}$$                           = 3 hours2). If Jamie's elevation is 600 feet while hiking up the mountain300 = $$\frac{600-0}{t-0}$$t = $$\frac{600}{300}$$t = 2 hours