Answer:
The distance he hiked up the canyon is;
[tex]6\text{ miles}[/tex]Explanation:
Let x represent his speed uphill;
So, since his speed downhill was 1 mph faster than his speed uphill.
his speed down hill is;
[tex]x+1[/tex]The distance uphill is equal to the distance downhill.
[tex]\text{distance}=\text{speed }\times\text{ time}[/tex]Given;
Time uphill = 3 hr
Time downhill = 2 hr
So, let us equate the distance up and down hill.
[tex]\begin{gathered} 3(x)=2(x+1) \\ 3x=2x+2 \\ \text{collect like terms} \\ 3x-2x=2 \\ x=2\text{ mph} \end{gathered}[/tex]Since the speed uphill is x which equals 2 mph.
The distance is;
[tex]\begin{gathered} \text{distance}=\text{speed uphill}\times Time\text{ uphill} \\ d=2\text{ mph}\times3\text{ hr} \\ d=6\text{ miles} \end{gathered}[/tex]Therefore, the distance he hiked up the canyon is;
[tex]6\text{ miles}[/tex]