At an isolated mountain camp, Emek and Tara discovered that a damaged water line was filling the storage tank too slowly. A gauge showed that only 7.5 liters had collected in 6 minutes. The camp needed 150 liters before the next group arrived in 90 minutes. Tara used the proportion 7.5/6 = 150/x and found that the tank would need 120 minutes to collect enough water at the current rate. That was 30 minutes beyond their deadline. Emek calculated that they needed a rate of 150/90, or about 1.67 liters per minute, instead of the current 1.25 liters per minute. They adjusted a partly closed valve and tested the line again. This time, the gauge collected 10 liters in 6 minutes, giving a rate of about 1.67 liters per minute. At that rate, 150 liters would take 90 minutes. They checked the proportion once more, then left the repaired line running. The tank reached the required level just as the arriving group approached the camp.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Convert 10/6 to a decimal and compare it with 1.25.
Before the valve was adjusted, the line filled the tank at 1.25 liters per minute. After the adjustment, it filled at 10/6 liters per minute. Which statement correctly compares the two rates?
The new rate is lower by about 0.42 liter per minute.The new rate is higher by about 0.42 liter per minute.The new rate is higher by exactly 1.25 liters per minute.The two rates are equal.
Correct! The new rate is about 1.67 liters per minute, which is about 0.42 liter per minute faster.
Not quite. Find the decimal value of 10/6 and subtract the original rate of 1.25 liters per minute.
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Hint
Compare 100 liters with the 10 liters collected every 6 minutes.
Suppose the camp needed only 100 liters of water after the valve was repaired. At the repaired rate of 10 liters every 6 minutes, how many minutes would it take to collect 100 liters?
Correct! Collecting 100 liters at 10 liters every 6 minutes takes 60 minutes.
Check how many groups of 10 liters are needed to reach 100 liters, then multiply by 6 minutes.
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Hint
Use the repaired rate to determine how long 150 liters takes, then compare that time with the new 80-minute deadline.
Suppose the group would arrive in 80 minutes instead of 90 minutes. Which statement correctly describes the repaired line if it still collected 10 liters every 6 minutes and the camp still needed 150 liters?
The repaired line would be sufficient because 150 liters would take 75 minutes.The repaired line would be sufficient because it would collect exactly 150 liters in 80 minutes.The repaired line would not be sufficient because 150 liters would still take 90 minutes, which is 10 minutes too long.The repaired line would not be sufficient because 150 liters would take 120 minutes.
Correct! The repaired line needs 90 minutes to collect 150 liters, so an 80-minute deadline would be too short.
Not quite. The repaired rate has not changed, so first determine the time needed for 150 liters and compare it with 80 minutes.
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Dağdaki Su Hattını Onarmak
TR
ARC_G10_FRD_02_STORY_02
Dağdaki Su Hattını Onarmak
Restoring the Mountain Water Line
EN
ARC_G10_FRD_02_STORY_02
Restoring the Mountain Water Line