Word problem, graphing. Please help...

[shileman]

The instructions say to show all work. I haven't a clue how to even start this problem.

[FONT=&quot]On a very sunny, beautiful day you decide to go hiking up a nearby mountain. When you near the top, there is a sign saying there are two ways to the summit. One way is a bit longer, but not as steep. The other is shorter, but steeper. Let’s imagine that you don’t mind steepness or distance, but you’ll take the route which has the smallest amount of ascending. Which route will you take and why?[/FONT]
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[FONT=&quot]The longer way, a 5% grade for 200 [/FONT][FONT=&quot]feet[/FONT][FONT=&quot], then 2% grade for 800 [/FONT][FONT=&quot]feet[/FONT][FONT=&quot], -2% grade for 400 [/FONT][FONT=&quot]feet[/FONT][FONT=&quot], 6% grade for 300 [/FONT][FONT=&quot]feet[/FONT][FONT=&quot], and a final grade of 4% for 400 ft.[/FONT]​

[FONT=&quot]The shorter way, an 8% grade for 600 ft. [/FONT]
​

 

[srmichael]

The instructions say to show all work. I haven't a clue how to even start this problem.

[FONT=&quot]On a very sunny, beautiful day you decide to go hiking up a nearby mountain. When you near the top, there is a sign saying there are two ways to the summit. One way is a bit longer, but not as steep. The other is shorter, but steeper. Let’s imagine that you don’t mind steepness or distance, but you’ll take the route which has the smallest amount of ascending. Which route will you take and why?[/FONT]


[FONT=&quot]The longer way, a 5% grade for 200 [/FONT][FONT=&quot]feet[/FONT][FONT=&quot], then 2% grade for 800 [/FONT][FONT=&quot]feet[/FONT][FONT=&quot], -2% grade for 400 [/FONT][FONT=&quot]feet[/FONT][FONT=&quot], 6% grade for 300 [/FONT][FONT=&quot]feet[/FONT][FONT=&quot], and a final grade of 4% for 400 ft.[/FONT]
[FONT=&quot]The shorter way, an 8% grade for 600 ft. [/FONT]
​

I agree with Denis. Be that as it may, though, "grade" just means slope. So for the first 200 feet, you would rise the amount that is 5% of 200 or 10 feet above from the original starting point 200 feet away. Keeping this in mind you can get the progressive locations of where you end after each route and then compare to where you end up on the 8% grade for 600 feet. I'll start you off:

5% grade for 200 feet = 10 feet higher
2% grade for 800 feet = 16 feet higher....WHICH MEANS YOU ARE NOW 26 FEET (10 + 16) HIGHER FROM YOUR ORIGINAL STARTING POSITION
-2% grade for 400 feet = 8 feet lower....(18 feet higher from original position (26 - 8)

continue...