Deep inside a newly discovered cave, Emek and Tara reached two passages leading toward the next chamber. Their map used a scale in which 2.5 centimeters represented 12 meters. The first passage measured 6.25 centimeters on the map, while the second measured 7.5 centimeters. Tara set up the proportion 2.5/12 = 6.25/x and found that the first passage was 30 meters long. Emek used the same scale to determine that the second passage was 36 meters long. Their notes showed that the first passage ended with an 4 meter vertical descent, while the second required a 3-meter descent. They had 35 meters of climbing rope, and safety rules required enough rope to cover the passage distance plus its descent. The first route would require 34 meters, while the second would require 39 meters, so they chose the shorter 30-meter passage and safely reached the next chamber.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Use both parts of the scale: 2.5 centimeters represents 12 meters.
A student claims that the first passage is 75 meters long because 6.25 * 12 = 75. Which statement correctly identifies the student's mistake?
The student should divide 6.25 by 12 because every map distance must be divided by the actual distance.The student should add 2.5 to 6.25 before using the scale.The student ignored that 12 meters corresponds to 2.5 centimeters, so the correct calculation is 6.25 * 12 / 2.5 = 30 meters.The student should subtract 2.5 from 6.25 and then multiply by 12.
Correct! The scale factor must account for the 2.5 centimeters that represents each 12 meters.
Not quite. Use the complete map scale rather than multiplying the map measurement directly by 12.
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Hint
Compare 5 centimeters with 2.5 centimeters, then apply the same factor to 12 meters.
A third passage measures 5 centimeters on the same map. Using the scale of 2.5 centimeters for 12 meters, how many meters long is the third passage?
Correct! A 5-centimeter map distance represents 24 meters.
Check how many groups of 2.5 centimeters fit into 5 centimeters, then multiply 12 meters by that number.
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Hint
Add the horizontal distances to the corresponding vertical distances.
Emek initially added each passage length to its vertical descent and concluded that neither route could be used with 35 meters of rope. Which statement correctly explains why this conclusion was wrong?
The map scale should not be used when comparing the two passages.One of the two routes require a rope length less than 35 meters.The passage distances should be divided by the descent distances before being compared with 35 meters.The 35 meters of rope should be added to each passage length before checking the descents.
Correct! When you add 30 meters(the horizontal distance) to its vertical distance(4 meters), you get 34 meters which is less than 35 meters.
Not quite. One of the routes require a rope length which is less than 35 meters.
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Mağara Geçidini Haritalamak
TR
ARC_G10_FRD_02_STORY_03
Mağara Geçidini Haritalamak
Mapping the Cave Passage
EN
ARC_G10_FRD_02_STORY_03
Mapping the Cave Passage