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Question 1118219: West of Albuquerque, New Mexico, Route 40 eastbound is straight and makes a steep descent towards the city, The highway has a 6% grade which means that its slope is -6/100. Driving on this road you notice from elevation signs that you have descended a distance of 100 ft. What is the change in our horizontal distance?
Found 4 solutions by Boreal, Alan3354, greenestamps, josgarithmetic:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! I was mistaken in that I thought the highway's percentage grade was elevation change divided by highway distance. It is the tangent, elevation change/ horizontal distance. But percentage is just percentage and not degrees. The road drops 6 feet for every 100 horizontal.
this is 6/100=100/x
6x=10000
x=1666.67 feet. horizontal distance ANSWER
The tangent is 0.06
This is 3.43 degrees.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! West of Albuquerque, New Mexico, Route 40 eastbound is straight and makes a steep descent towards the city, The highway has a 6% grade which means that its slope is -6/100. Driving on this road you notice from elevation signs that you have descended a distance of 100 ft. What is the change in our horizontal distance?
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Use a right triangle.
Vertical leg = 100 feet
tan(6) = 100/horizontal
horizontal distance = 100/tan(6) =~ 951.4 feet
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
You have two very different answers from different tutors, resulting from different interpretations of the question as you present it.
The phrase "descended a distance of 100 feet" is awkward, and open to (at least) three possible interpretations:
(1) you traveled 100 feet on the road and want to know your change in elevation;
(2) the elevation has changed by 100 feet and you want to know how far you have traveled along the road; or
(3) the elevation has changed by 100 feet and you want to know the horizontal distance you have traveled.
The fact that the problem says you know what is happening because of elevation signs along the highway makes it seem that (1) can't be the correct interpretation, because the elevation signs won't tell you when you have traveled 100 feet.
On the other hand, while I have seen elevation signs on highways in increments of 1000 feet of elevation, I doubt that there are places where elevation changes of 100 feet are marked by highway signs.
In the end, you quite possibly are not getting the help you wanted with the problem, because you were not careful with your presentation of the problem.
Answer by josgarithmetic(39613)  (Show Source):
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