Math Problem Statement

A reservoir has the following inflows and outflows (in cubic meters) for the first three months of the year. If the storage at the beginning of January is 65 m³, determine the storage at the end of March. Month | January | February | March --- | --- | --- | --- Inflow | 2 | 3 | 4.5 Outflow | 4 | 5.5 | 2.5

Solution

Let's solve the problem.

We are given:

  • Initial storage at the beginning of January: 65 m³
  • Inflows and outflows for three months.

The task is to calculate the storage at the end of March.

Step-by-step solution:

The storage at the end of each month is calculated as: Storage at end of the month=Storage at start of the month+InflowOutflow.\text{Storage at end of the month} = \text{Storage at start of the month} + \text{Inflow} - \text{Outflow}.

January:

End of January storage=65+24=63.\text{End of January storage} = 65 + 2 - 4 = 63 \, \text{m³}.

February:

End of February storage=63+35.5=60.5.\text{End of February storage} = 63 + 3 - 5.5 = 60.5 \, \text{m³}.

March:

End of March storage=60.5+4.52.5=62.5.\text{End of March storage} = 60.5 + 4.5 - 2.5 = 62.5 \, \text{m³}.

Final Answer:

The storage at the end of March is 62.5 m³.

Would you like a breakdown of any specific step or further explanation?


Here are 5 follow-up questions to expand on this:

  1. What would the storage be if the inflow or outflow changed in one of the months?
  2. How would you account for evaporation or additional losses in the reservoir system?
  3. What if the storage at the beginning of January was different? How would that impact the results?
  4. Could you predict the storage for subsequent months if the inflow and outflow trends continued?
  5. How can this calculation be applied in real-life water management scenarios?

Tip: Always check your units (e.g., cubic meters, liters) when working with inflows, outflows, and storage to ensure consistency.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Operations
Net Change Calculation

Formulas

Storage at end of the month = Storage at start of the month + Inflow - Outflow

Theorems

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Suitable Grade Level

Grades 6-8