Question: 408
3. Mount Fuji in Japan was first climbed by a monk in 663 AD and subsequently became a Japanese religious site for hundreds of years. It is now a popular tourist site. When ascending the mountain, tourists drive part of the distance and climb the rest of the way. Suppose a tourist drove to an elevation of 2,390 meters and from that point climbed to the top of the mountain, and then descended back to the car taking the same route. If it took her a total of 7 hours to climb up and back down, and she climbed at an average rate of 264 vertical meters per hour going up and twice that going down, approximately how tall is Mount Fuji?
A. 1,386 meters
B. 2,772 meters
C. 3,776 meters
D. 5,172 meters
Correct Answer: C
Explanation:
C
Difficulty: Medium
Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages
Strategic Advice: There are a few ways to answer this question, but the quickest way is to average the tourist’s climb rate over the 7 hours.
Getting to the Answer: The distance going up and back down is the same (because she uses the same route), so find the average of the tourist’s speed over both the ascent and the descent. She climbed 264 meters per hour going up and twice that, 528 meters per hour, going back down, so her average climb rate was 264 + 528 = 792 ÷ 2 = 396 meters per hour. It took her 7 hours. Use the formula Distance = rate × time to find the distance:
But remember, this amount represents both up and down the mountain, so divide by 2 to find that the vertical distance between the point where she started climbing and the top of the mountain is 1,386 meters. Be careful—this is not the answer! The question asks how tall Mount Fuji is, so don’t forget to add the vertical distance she drove, 2,390 meters, to get 2,390 + 1,386 = 3,776 meters.
How did they find the average of speeds by simply finding the arithmetic mean? This is incorrect, unless we have equivalent time. Shouldn’t they have used the harmonic mean instead?