While guiding a caravan across the desert, Emek and Tara studied an old map that related travel distances to water supplies using constant ratios. One section showed that 24 liters of water were needed for every 40 kilometers of travel. A later checkpoint required a 70-kilometer journey, but the required water amount was missing from the map. They used proportional reasoning to calculate the missing value, then compared the ratios for each stage to confirm the plan remained consistent. Their careful adjustments ensured the caravan reached the final oasis with enough water for every traveler.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Set up a proportion using liters per kilometer.
The map shows that 24 liters of water are needed for every 40 kilometers. How many liters are needed for a 70-kilometer journey?
40 liters42 liters44 liters48 litersCorrect! A 70-kilometer journey requires 42 liters of water.
Use the constant ratio of 24 liters for every 40 kilometers.
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Hint
First find the liters needed for 1 kilometer, then multiply by 100.
If another section of the route is 100 kilometers long, how many liters of water are needed to keep the same ratio?
Correct! The caravan needs 60 liters.
Keep the ratio of 24 liters for every 40 kilometers.
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Hint
Calculate the required amount for 70 kilometers before comparing it with 45 liters.
A traveler suggests taking 45 liters of water for the 70-kilometer trip. Which statement is correct?
45 liters is correct because it is close to 42 liters.45 liters is too little because the trip needs 48 liters.45 liters is more than required because the proportional calculation gives 42 liters.45 liters is correct because longer trips do not need proportional reasoning.Correct! The required amount is 42 liters, so 45 liters is more than necessary.
Find the correct amount using the given ratio, then compare it with 45 liters.
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