Question 39·Hard·Ratios, Rates, Proportional Relationships, and Units
The table lists the number of the twenty-five largest seawater-desalination plants operating worldwide in 2022, categorized by location and maximum daily output.
| Region | Low | Medium | High | Total |
|---|---|---|---|---|
| Middle East | 1 | 2 | 3 | 6 |
| North America | 3 | 2 | 1 | 6 |
| Europe | 2 | 1 | 1 | 4 |
| Asia–Pacific | 2 | 1 | 2 | 5 |
| Africa | 1 | 1 | 0 | 2 |
| South America | 1 | 0 | 1 | 2 |
| Total | 10 | 7 | 8 | 25 |
The combined maximum daily output of the six Middle East plants is 580 million liters. The combined maximum daily output of all twenty-five plants is 1,920 million liters.
If each of the six Middle East plants operated at its maximum rate every day for 30 consecutive days, approximately how many billion liters of freshwater would they produce during that period?
For questions involving rates and time, first isolate the relevant group or category (here, just the six Middle East plants), then multiply the combined rate by the time period to get a total. After that, carefully convert units (such as from million to billion by dividing by 1,000) and only then compare to the answer choices, checking that your result is a reasonable size (large industrial processes over many days should not give very tiny numbers).
Hints
Focus on which plants and which rate
Make sure you are only using the information about the six Middle East plants and their combined maximum daily output of 580 million liters. Ignore the data about all 25 plants for this question.
Use rate × time
You know how much water the six plants produce per day. How do you use that to find how much they produce in 30 days at the same rate?
Pay attention to units (million vs. billion)
Your first calculation will give an answer in million liters. What conversion do you need to do to express that amount in billion liters?
Think about the size of the answer
After converting to billion liters, check if your number makes sense: producing at a huge industrial scale for 30 days should give a number greater than 1 billion liters, not a small fraction.
Desmos Guide
Calculate the 30-day total in million liters
In Desmos, type 580*30 and look at the result. This is the total number of million liters produced in 30 days by the six Middle East plants.
Convert the result to billion liters
In a new Desmos expression, type (580*30)/1000. This divides the 30-day total in million liters by 1,000 to convert to billion liters. Compare this decimal value to the answer choices and choose the one that matches it when rounded to the nearest whole number.
Step-by-step Explanation
Identify what the 580 million liters represents
The problem states that the combined maximum daily output of the six Middle East plants is 580 million liters.
That means all six plants together produce 580 million liters per day when running at maximum capacity.
Compute the total output for 30 days (still in millions)
To find how much water these plants produce in 30 days at maximum rate, multiply the daily output by 30:
This gives the total number of million liters produced over 30 days by the six plants.
Convert from million liters to billion liters
The result from Step 2 is in million liters. The question asks for the amount in billion liters.
Remember:
- billion liters million liters.
So to convert your 30-day total from million liters to billion liters, divide by 1,000:
This gives the total in billion liters.
Round to match the answer choices
When you multiply , you get million liters.
Convert to billion liters:
The question asks for an approximate amount, so round to the nearest whole number: 17 billion liters. Therefore, the correct answer is 17.