Beneath an abandoned fortress, Emek and Tara reached a stone passage flooded by rising water. An old control panel showed that the drainage system could make the passage safe, but they had to determine how long to run it. The panel modeled the water level with 4.8 - 0.3(t - 2) = 2.1, where t was the total operating time in minutes and 2.1 meters was the safe level. Tara first subtracted 4.8 from both sides, giving -0.3(t - 2) = -2.7. Emek divided both sides by -0.3 to obtain t - 2 = 9, so t = 11 minutes. They checked the result by substituting 11 into the original equation: 4.8 - 0.3(9) = 2.1. The equality was correct. Emek set the system for 11 minutes, and the water steadily dropped to the marked safe level. With the passage clear enough to cross, they continued their exploration.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Subtract 4.8 from each side and carefully determine the sign of 2.1 - 4.8.
In the equation 4.8 - 0.3(t - 2) = 2.1, Tara subtracts 4.8 from both sides. Which equation correctly represents the result?
-0.3(t - 2) = 2.70.3(t - 2) = -2.7-0.3(t - 2) = -2.7-0.3(t - 2) = -6.9
Correct. Subtracting 4.8 from both sides gives -0.3(t - 2) = -2.7.
Not quite. Check both the subtraction 2.1 - 4.8 and the negative sign already attached to 0.3.
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Hint
Isolate the term containing t, divide by -0.3, and then solve for t.
Suppose the team later needs the water level to reach 1.5 meters instead of 2.1 meters. Using the same model, 4.8 - 0.3(t - 2) = 1.5, how many total minutes should the drainage system operate?
Correct. The drainage system must operate for 13 minutes.
Check each inverse operation carefully, especially when dividing by -0.3.
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Hint
Compare the two operating times and multiply the difference by the 0.3-meter change per minute.
The original safe level of 2.1 meters requires 11 minutes of operation. The new target of 1.5 meters requires 13 minutes. Which statement best connects these results to the model?
The extra 2 minutes reduce the water level by 0.6 meter because the model decreases the level by 0.3 meter per additional minute.The extra 2 minutes reduce the water level by 2 meters because each minute changes the level by 1 meter.The water level rises by 0.6 meter because t increases from 11 to 13.The two operating times should be equal because both equations use the same model.
Correct. Two additional minutes lower the modeled water level by 2 * 0.3 = 0.6 meter.
Not quite. Use the difference between 13 and 11 minutes together with the model's 0.3-meter change per minute.
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Yeraltı Su Odası
TR
ARC_G10_OPS_02_STORY_02
Yeraltı Su Odası
The Underground Water Chamber
EN
ARC_G10_OPS_02_STORY_02
The Underground Water Chamber