Tyler will hike 3,600 feet to reach the summit and it will take him 0.34 hours.
Tyler will have to hike 3,600 feet to reach the summit of the mountain.
To determine this, we can set up a proportion based on the ratio of the heights of the two mountains:
6/5 = x/3000
where x represents the distance Tyler needs to hike. Solving for x, we get:
x = (6 * 3000) / 5 = 3600 feet
It will take Tyler 0.34 minutes to hike to the summit of the mountain if he hikes at a rate of 2 miles per hour.
First, we need to convert the distance to miles and the rate to miles per hour:
3,600 feet * (1 mile/5,280 feet) = 0.68 miles
2 miles/hour * (60 minutes/hour) = 120 minutes/hour
Using the formula time = distance/rate, we can calculate the hiking time:
time = 0.68 miles / 120 minutes/hour = 0.0057 hours
Converting hours to minutes:
0.0057 hours * (60 minutes/hour) = 0.34 minutes
Therefore, it will take Tyler 0.34 minutes to reach the summit of the mountain.
Complete question below:
2.7.4 Practice: Modeling: Similarity Theorems
About Face! Your Peak of Choice
Your friend Tyler is a mountain climber. He wants to climb a peak that is 6,000 feet tall. He has been training for his climb and is now ready to start.
Tyler knows that the mountain he wants to climb is similar to a mountain he has already climbed. The mountain he has already climbed is 5,000 feet tall. The ratio of the height of the two mountains is 6:5.
Tyler also knows that the distance from the base of the mountain to the summit is 3,000 feet.
Questions:
How far will Tyler have to hike to reach the summit of the mountain?
How long will it take Tyler to hike to the summit of the mountain if he hikes at a rate of 2 miles per hour?