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Josh is hiking Glacier National Park. He has now hiked a total of 17km and is 2km short of being (1)/(2) of the way done with his hike. If h is the total length of Josh's hike, which of the following equations best describes the situation? Choose 1 answer: (A) (1)/(2)h-2=17 (B) (1)/(2)h+2=17 (C) 2h-2=17 (D) 2h+2=17

Josh is hiking Glacier National Park. He has now hiked a total of 17 km 17 \mathrm{~km} and is 2 km 2 \mathrm{~km} short of being 12 \frac{1}{2} of the way done with his hike. If h h is the total length of Josh's hike, which of the following equations best describes the situation?\newlineChoose 11 answer:\newline(A) 12h−2=17 \frac{1}{2} h-2=17 \newline(B) 12h+2=17 \frac{1}{2} h+2=17 \newline(C) 2h−2=17 2 h-2=17 \newline(D) 2h+2=17 2 h+2=17

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Q. Josh is hiking Glacier National Park. He has now hiked a total of 17 km 17 \mathrm{~km} and is 2 km 2 \mathrm{~km} short of being 12 \frac{1}{2} of the way done with his hike. If h h is the total length of Josh's hike, which of the following equations best describes the situation?\newlineChoose 11 answer:\newline(A) 12h−2=17 \frac{1}{2} h-2=17 \newline(B) 12h+2=17 \frac{1}{2} h+2=17 \newline(C) 2h−2=17 2 h-2=17 \newline(D) 2h+2=17 2 h+2=17
  1. Step 11: Establishing the halfway point: Josh has hiked 17 km17\,\text{km} and is 2 km2\,\text{km} short of being half of the way done with his hike. To find the total length of the hike, we need to express the half-way point in terms of the total length hh, and then account for the 2 km2\,\text{km} that he is short of that half-way point.
  2. Step 22: Accounting for the distance Josh is short: Let's denote the total length of the hike as hh. Being half-way done would be represented by (12)h(\frac{1}{2})h. Since Josh is 2 km2\,\text{km} short of this half-way point, we need to add 2 km2\,\text{km} to the distance he has already hiked to equal the half-way point. Therefore, the equation that represents the situation is (12)h=17 km+2 km(\frac{1}{2})h = 17\,\text{km} + 2\,\text{km}.
  3. Step 33: Setting up the equation: Simplifying the equation, we get (12)h=19 km(\frac{1}{2})h = 19 \text{ km}. This equation shows that half of the total length of the hike is 19 km19 \text{ km}, which means that the total length is twice this amount.
  4. Step 44: Simplifying the equation: To find the total length hh, we multiply both sides of the equation by 22 to get h=2×19 kmh = 2 \times 19 \text{ km}.
  5. Step 55: Finding the total length of the hike: After performing the multiplication, we find that h=38 kmh = 38\,\text{km}. This means that the total length of Josh's hike is 38 km38\,\text{km}.
  6. Step 66: Matching the equation with the options: Now, we need to match our equation with the given options. The correct equation that we derived is (12)h=19(\frac{1}{2})h = 19, which can be rewritten as (12)h−2=17(\frac{1}{2})h - 2 = 17 to match the format of the options. This corresponds to option (A).

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