i need help to find the elevation of the roasd begins at the piont where the road begins

Question

A mountian road is 5 miles long and gains elevation at a constant rate.After 2 miles,the elvation is 5500 feet above sea level.After 4 miles,the elevation is 6200 feet above sea level.

Answer 1

I am assuming you want to know what the beginning elevation is?

 

Defining constant elevation rate = (change in height or elevation)/(change in distance) 

 

Let h0 - initial elevation (ft above sea level)

 

     h1 = 5500 ft above sea level

 

     h2 = 6200 ft above sea level

 

For first leg:

 

elevation rate = (h1 - h0)/2 miles = constant

 

For  2nd leg:

 

elevation rate = (h2 - h1)/4 miles

 

Setting equal to each other and solving for h0:

 

(h1 - h0)/2 = (h2 - h1)/4

 

Multiplying both sides by 4:

 

2*(h1 - h0) = h2 - h1

 

2*h1 - 2*h0 = h2 - h1

 

3*h1 - h2 = 2*h0

 

or rearranging.

 

2*h0 = 3*h1 - h2

 

h0 = (3*h1 - h2)/2 = (3*5500 - 6200)/2 = 5150 ft above sea level