A municipal utility operates three water desalination plants—Plant Alpha, Plant Beta, and Plant Gamma—to process seawater into purified drinking water. Each plant operates at a constant total intake rate of seawater and yields a specific percentage of brine byproduct, with the remainder converted to purified drinking water:
- Plant Alpha: Total intake rate of gallons per hour; of intake becomes brine byproduct.
- Plant Beta: Total intake rate of gallons per hour; of intake becomes brine byproduct.
- Plant Gamma: Total intake rate of gallons per hour; of intake becomes brine byproduct.
Match each operational metric on the left with its corresponding calculated value on the right.
- The combined purified drinking water output rate of Plant Alpha and Plant Beta operating simultaneously (in thousands of gallons per hour). thousand gallons per hour
- The ratio of the total volume of brine byproduct produced by Plant Alpha in hours to the total volume of brine byproduct produced by Plant Gamma in hours.
- The total operational time (in hours) required for Plant Beta to produce the exact volume of purified drinking water that Plant Gamma produces in hours. hours
Answer
The operational metrics match as follows: the combined output rate of Plant Alpha and Plant Beta is thousand gallons per hour; the ratio of brine byproduct volume produced by Plant Alpha (in 5 hours) to Plant Gamma (in 4 hours) is ; and the time required for Plant Beta to equal Plant Gamma's 9-hour purified output is hours.
Each calculation requires decomposing total plant intake into its constituent components (purified water and brine byproduct) using given percentages, followed by executing standard work-rate and ratio operations (). The resulting values match thousand gallons per hour, , and hours respectively.
Step-by-Step Solution
Key Concept
Work rates and percent composition decomposition in multi-unit processing systems.
Estimated Time:2m 30s