Problem 107 - Elementary Algebra

Question

Find the number of gallons delivered per day from the wells to Brantley Reservoir, The Seven Rivers well field ... and an additional three private wells can produce about 20,000 gallons of water per minute that is delivered through a 12 -mile pipeline network directly to Brantley Reservoir located about 12 miles north of Carlsbad. (Source: www.currentargus.com, Sept. 10, 2009)

Step-by-Step Solution

Answer

28,800,000 gallons per day

Step 1 - Understand the Problem

The task requires converting the flow rate of water from the wells, given in gallons per minute, to the total number of gallons delivered per day.

Step 2 - Identify the Given Values

The water production rate is given as 20,000 gallons per minute.

Step 3 - Convert Minutes to Hours

There are 60 minutes in an hour. Multiply the flow rate by 60 to find the number of gallons delivered per hour: \[ 20,000 \text{ gallons/minute} \times 60 \text{ minutes/hour} = 1,200,000 \text{ gallons/hour} \]

Step 4 - Convert Hours to Days

There are 24 hours in a day. Multiply the hourly delivery rate by 24 to find the number of gallons delivered per day: \[ 1,200,000 \text{ gallons/hour} \times 24 \text{ hours/day} = 28,800,000 \text{ gallons/day} \]

Key Concepts

flow rate

Flow rate is a crucial concept in many disciplines, especially in fluid dynamics and engineering. It describes the volume of fluid that moves through a system per unit of time. In this exercise, the flow rate is given as 20,000 gallons per minute (gpm).

Understanding flow rate helps us determine how quickly a resource is being replenished or depleted. For example, in water resource management, knowing the flow rate of water into a reservoir can help managers make decisions about water use, conservation, and distribution.

To convert flow rate into different time units properly, it's important to be clear on the volume (gallons) and the time unit (minutes) being used. We will use these concepts to calculate the total gallons delivered to Brantley Reservoir each day.

gallons per minute

Gallons per minute (gpm) is a unit of flow rate commonly used in the United States. It tells us how many gallons of a fluid (water in this case) pass through a system each minute.

In this exercise, the given flow rate is 20,000 gpm. This means that every minute, 20,000 gallons of water are pumped into the pipeline network heading to Brantley Reservoir.

Understanding and calculating with gpm is crucial for engineering tasks, allowing for the planning of systems that can handle the required flow without being overwhelmed.

minutes to hours conversion

To convert the flow rate from minutes to hours, we need to know how many minutes are in an hour, which is 60. We start with 20,000 gallons per minute:

• 1 minute = 60 seconds
• 1 hour = 60 minutes

So, we multiply the flow rate by 60 to convert to gallons per hour:
\( 20,000 \text{ gallons/minute} \times 60 \text{ minutes/hour} = 1,200,000 \text{ gallons/hour} \)
This calculation tells us that every hour, 1,200,000 gallons of water flow into the reservoir.

hours to days conversion

Next, we convert the flow rate from hours to days. There are 24 hours in a day, so we use this conversion factor:

• 1 day = 24 hours

Multiply the hourly flow rate by 24 to find the daily flow rate:
\( 1,200,000 \text{ gallons/hour} \times 24 \text{ hours/day} = 28,800,000 \text{ gallons/day} \)
This result means that 28,800,000 gallons of water are delivered to Brantley Reservoir each day. Breaking down the conversions into these steps helps make sense of large quantities over extended time periods.