Question

You are hiking a six-mile trail at a constant rate in Topanga Canyon. You begin at 10 A.M. At noon you are two miles from the end of the trail. Find the distance you are from the end of the trail at \(11 \mathrm{A} . \mathrm{M}\)

Short answer

The distance from the end of the trail at 11 AM is 4 miles.

Step-by-step solution

Determine the distance traveled

Between 10 AM and 12 PM, two hours passed. At noon, two miles remain, so in the two hours, four miles (six-mile trail minus two miles remaining) were traveled.

Determine the speed

Divide the distance traveled (four miles) by the time taken (two hours) to get the speed: \( \frac{4 miles}{2 hours} = 2mph \)

Find the remaining distance at 11 AM

If the hike started at 10 AM and it's currently 11 AM, one hour has passed. Given the speed was found to be 2mph, 2 miles have been traveled. So, the distance remaining from the end of the trail would be 4 miles (Total trail distance 6 miles minus 2 miles traveled).