Math Problem Statement

Debra pumped 12 gallons of water out of her pool. This was done over a period of 2 minutes at a constant rate. What was the change in the amount of water in the pool each minute?

Solution

To find the change in the amount of water in the pool each minute, we need to calculate the rate at which Debra pumped the water out of the pool.

Given Information:

  • Total water pumped out: 12 gallons
  • Time taken: 2 minutes

Calculation:

The rate at which Debra pumped water out of the pool (in gallons per minute) can be calculated by dividing the total amount of water pumped by the total time:

Rate of water pumped out=Total water pumped outTime taken\text{Rate of water pumped out} = \frac{\text{Total water pumped out}}{\text{Time taken}}

Substitute the given values:

Rate of water pumped out=12gallons2minutes=6gallons per minute\text{Rate of water pumped out} = \frac{12 \, \text{gallons}}{2 \, \text{minutes}} = 6 \, \text{gallons per minute}

Answer:

The change in the amount of water in the pool each minute is 6 gallons per minute.

Would you like more details or have any other questions? Here are five related questions to explore further:

  1. How would you find the total time required to pump out 30 gallons at the same rate?
  2. What would be the change in rate if the water was pumped out in 3 minutes instead?
  3. How can this rate be converted to gallons per second?
  4. How would you calculate the rate if the amount of water pumped changes periodically?
  5. Can you explain why understanding constant rates is useful in real-world situations?

Tip: When dealing with rates, always ensure that the units are consistent to avoid calculation errors.