SOLUTION: For purposes of this exercise, we will think of the Mississippi River as a straight line beginning at its headwaters, Lake Itasca, Minnesota, at an elevation of 1475 feet above se

Question 363828: For purposes of this exercise, we will think of the Mississippi River as a straight line beginning at its headwaters, Lake Itasca, Minnesota, at an elevation of 1475 feet above sea level, and sloping downward to the Gulf of Mexico 2340 miles to the south.
(a) Think of the southern direction as pointing right along the horizontal axis. What is the slope of the line representing the Mississippi River? Express your answer in foot per mile.
m=rise/run = 1475/2340= 0.63 Answer: -0.63
(b) Memphis, Tennessee, sits on the Mississippi River 1982 miles south of Lake Itasca. What is the elevation of the river as it passes Memphis?
__________________________________ I tried 0.63*1982 and got the answer wrong.
(c) How many miles south of Lake Itasca would you find the elevation of the Mississippi to be 500 feet?
__________________________________ Being I can't get part (b) I have been
struggling with part (c).

Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
For purposes of this exercise, we will think of the Mississippi River as a straight line beginning at its headwaters, Lake Itasca, Minnesota, at an elevation of 1475 feet above sea level, and sloping downward to the Gulf of Mexico 2340 miles to the south.
(a) Think of the southern direction as pointing right along the horizontal axis. What is the slope of the line representing the Mississippi River? Express your answer in foot per mile.
m=rise/run = 1475/2340= 0.63 Answer: -0.63
(b) Memphis, Tennessee, sits on the Mississippi River 1982 miles south of Lake Itasca. What is the elevation of the river as it passes Memphis?
I tried 0.63*1982 and got the answer wrong.
The slope is -0.63
The decrease in elevation = 1982*(-0.63) = -1249 feet
Then the elevation of Memphis = 1475 - 1249 = 226 ft
------------------------------------------
(c) How many miles south of Lake Itasca would you find the elevation of the Mississippi to be 500 feet?
The change is 1475 - 500 = 975 feet
975 = m*distance in miles
d = 975/m = 1547 miles
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For purposes of this exercise, we will think of the Mississippi River as a straight line beginning at its headwaters, Lake Itasca, Minnesota, at an elevation of 1475 feet above sea level, and sloping downward to the Gulf of Mexico 2340 miles to the south.
==========
(a) Think of the southern direction as pointing right along the horizontal axis. What is the slope of the line representing the Mississippi River? Express your answer in foot per mile.
---
Draw the picture on a coordinate system and you will
see that the slope is negative.
---
m=rise/run = -1475/2340= -0.63 Answer: -0.63
==========

(b) Memphis, Tennessee, sits on the Mississippi River 1982 miles south of Lake Itasca. What is the elevation of the river as it passes Memphis?
Put a point at (1982,0) on your picture.
Notice the similar triangles.
Develop a proportion relating rise/run at the x = 1982.
---
Solve:
rise/(2340-1982) = 1475/2340
rise = 0.63*378 = 225,54 ft.
-----------------------------------

(c) How many miles south of Lake Itasca would you find the elevation of the Mississippi to be 500 feet?
---
Solve:
run/500 = 2350/1475
run = 500*1.59
run = 796.61 miles
----
Question for you. Is that point 796 miles from the
Gulf, or is it 796 from Lake Itasca?
---------------
Cheers,
Stan H.

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