Question

Practice: Bryan hiked up to the top of City Creek in 3 hr and then returned down the canyon to the trailhead in another 2 hr. His speed downhill was 1 mph faster than his speed uphill. How far up the canyon did he hike?

Answer 1

The distance he hiked up the canyon is;

`6\text{ miles}`

Step-by-step 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;

`x+1`

The distance uphill is equal to the distance downhill.

`\text{distance}=\text{speed }*\text{ time}`

Given;

Time uphill = 3 hr

Time downhill = 2 hr

So, let us equate the distance up and down hill.

`\begin{gathered} 3(x)=2(x+1) \\ 3x=2x+2 \\ \text{collect like terms} \\ 3x-2x=2 \\ x=2\text{ mph} \end{gathered}`

Since the speed uphill is x which equals 2 mph.

The distance is;

`\begin{gathered} \text{distance}=\text{speed uphill}* Time\text{ uphill} \\ d=2\text{ mph}*3\text{ hr} \\ d=6\text{ miles} \end{gathered}`

Therefore, the distance he hiked up the canyon is;

`6\text{ miles}`