You are hiking on a trail that leads to the top of a mountain. At 1 P.M. you reach an elevation of 4400 feet. At 4 P.M. you reach an elevation of 5600 feet. What is your mean hourly change in elevation?
Let
t = time, hours
h = height, feet
At 1 PM, the time and height are respectively
t₁ = 1 hour
h₁ = 4400 feet
At 4 PM, the time and height are respectively
t₂ = 4 hours
h₂ = 5600 feet
By definition, the mean hourly change in elevation is
\(\frac{h_{2} - h_{1}}{t_{2} - t_{1}} = \frac{5600-4400}{4-1} = \frac{1200}{3} =400\)
Answer: 400 feet per hour