Question

1. you and your friend start walking from different locations on a 10-mile hiking trail. you start at the trailhead and walk 4 miles per hour. your friend starts 4 miles from the trailhead and walks 2.5 miles per hour. who will reach the end of the trail first?

Explanation:

Step1: Calculate your time

The distance you need to walk is 10 miles (since you start at the trailhead), and your speed is 4 miles per hour. Using the formula \( t = \frac{d}{v} \) (time = distance / speed), your time \( t_1 \) is \( \frac{10}{4} = 2.5 \) hours.

Step2: Calculate your friend's time

Your friend starts 4 miles from the trailhead, so the distance your friend needs to walk is \( 10 - 4 = 6 \) miles. Your friend's speed is 2.5 miles per hour. Using the same time formula, your friend's time \( t_2 \) is \( \frac{6}{2.5} = 2.4 \) hours.

Step3: Compare the times

Now we compare \( t_1 = 2.5 \) hours and \( t_2 = 2.4 \) hours. Since \( 2.4 < 2.5 \), your friend's time is less.

Answer:

Your friend will reach the end of the trail first.