While helping restore an ancient aqueduct, Emek and Tara learned that every stone channel had been built using the same width-to-depth ratio. They compared measurements from each restored section and checked whether the proportions matched the original design. One rebuilt segment had dimensions that broke the pattern, even though it looked correct at first. After identifying the incorrect section, they calculated the proper proportional measurements and rebuilt it. When water flowed smoothly through the entire aqueduct, the restoration team reopened the system, preserving both its function and its historical design.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Simplify each width-to-depth ratio and compare it with 6:4.
The original aqueduct used a width-to-depth ratio of 6:4. Which rebuilt section does NOT match the original design?
Width 9 m, Depth 6 mWidth 12 m, Depth 8 mWidth 15 m, Depth 9 mWidth 18 m, Depth 12 mCorrect! Only 15:9 does not simplify to the same ratio as 6:4.
Reduce each ratio to its simplest form before comparing.
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Hint
Use a proportion based on the ratio 6:4.
A rebuilt section has a width of 21 meters. If it must keep the original width-to-depth ratio of 6:4, what should its depth be, in meters?
Correct! A depth of 14 meters keeps the ratio unchanged.
Set up a proportion using the original width-to-depth ratio.
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Hint
Find the correct depth that matches a width of 24 meters using the original ratio.
A worker rebuilt one section with a width of 24 meters and a depth of 18 meters. To match the original ratio of 6:4, what should be changed?
Decrease the depth to 16 meters.Decrease the width to 20 meters.Increase the width to 27 meters.No change is needed.Correct! A width of 24 meters should have a depth of 16 meters.
Use the original ratio to calculate the correct depth before deciding.
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