Josh is hiking Glacier National Park. He has now hiked a total of [tex]17 \text{ km}[/tex] and is [tex]2 \text{ km}[/tex] short of being [tex]\frac{1}{2}[/tex] of the way done with his hike.

Write an equation to determine the total length in kilometers [tex](h)[/tex] of Josh's hike.
[tex]\[
\square
\][/tex]



Answer :

Let's denote the total length of Josh's hike by \( h \).

Given:
1. Josh has hiked a total of 17 km so far.
2. He is 2 km short of being halfway done with his hike.

From this information, we can set up an equation to find \( h \).

Since Josh is 2 km short of being halfway done, we can express his progress as:
[tex]\[ 17 \, \text{km} = \left( \frac{h}{2} - 2 \, \text{km} \right) \][/tex]

We need to solve for \( h \).

Step-by-step solution:
1. Start by setting up the equation based on the information given:
[tex]\[ 17 = \frac{h}{2} - 2 \][/tex]

2. To eliminate the fraction, add 2 to both sides of the equation:
[tex]\[ 17 + 2 = \frac{h}{2} \][/tex]
[tex]\[ 19 = \frac{h}{2} \][/tex]

3. Next, solve for \( h \) by multiplying both sides of the equation by 2:
[tex]\[ 19 \times 2 = h \][/tex]
[tex]\[ h = 38 \][/tex]

Therefore, the total length in kilometers of Josh's hike is [tex]\( \boxed{38} \)[/tex].