Answer :
Let's break down the problem step by step to find out how much time it will take to fill the pool 6 inches from the top.
### Step 1: Determine the Volume of the Pool
First, compute the volume of the pool. We are given that the length of the pool is 15 feet, the width is 30 feet, and the depth to fill is 6 inches from the top.
Since 6 inches is half of a foot (because 1 foot = 12 inches), we can express the depth to fill in feet:
- Depth in feet = 6 inches / 12 inches per foot = 0.5 feet
The volume of the pool can be calculated using the formula for the volume of a rectangular prism:
- Volume = Length × Width × Depth
- Volume = 15 feet × 30 feet × 0.5 feet
So, the volume of the pool in cubic feet is:
- Volume = 15 × 30 × 0.5 = 225 cubic feet
### Step 2: Convert the Volume to Gallons
Next, we need to convert the volume from cubic feet to gallons. We are given that 1 cubic foot is equivalent to 7.48 gallons:
- Volume in Gallons = Volume in Cubic Feet × Gallons per Cubic Foot
- Volume in Gallons = 225 cubic feet × 7.48 gallons per cubic foot
So, the volume of the pool in gallons is:
- Volume in Gallons = 225 × 7.48 = 1683 gallons
### Step 3: Calculate the Time Needed to Fill the Pool
Now, we need to calculate the time required to fill the pool. The hose dispenses water at a rate of 10.5 gallons per minute. Using this rate, we can find the time needed to fill the pool by dividing the total volume of the pool by the rate of the hose:
- Time in Minutes = Volume in Gallons / Hose Rate in Gallons per Minute
- Time in Minutes = 1683 gallons / 10.5 gallons per minute
So, the time needed in minutes is:
- Time in Minutes = 1683 / 10.5 ≈ 160.29 minutes
### Step 4: Convert Time to Hours
Finally, we need to convert the time from minutes to hours and round to the nearest hour. There are 60 minutes in one hour:
- Time in Hours = Time in Minutes / 60
- Time in Hours = 160.29 minutes / 60 minutes per hour ≈ 2.67 hours
Rounding 2.67 hours to the nearest whole number, we get:
- Time in Hours ≈ 3 hours
So, it will take approximately 3 hours to fill the pool 6 inches from the top using a garden hose that dispenses water at a rate of 10.5 gallons per minute.
### Step 1: Determine the Volume of the Pool
First, compute the volume of the pool. We are given that the length of the pool is 15 feet, the width is 30 feet, and the depth to fill is 6 inches from the top.
Since 6 inches is half of a foot (because 1 foot = 12 inches), we can express the depth to fill in feet:
- Depth in feet = 6 inches / 12 inches per foot = 0.5 feet
The volume of the pool can be calculated using the formula for the volume of a rectangular prism:
- Volume = Length × Width × Depth
- Volume = 15 feet × 30 feet × 0.5 feet
So, the volume of the pool in cubic feet is:
- Volume = 15 × 30 × 0.5 = 225 cubic feet
### Step 2: Convert the Volume to Gallons
Next, we need to convert the volume from cubic feet to gallons. We are given that 1 cubic foot is equivalent to 7.48 gallons:
- Volume in Gallons = Volume in Cubic Feet × Gallons per Cubic Foot
- Volume in Gallons = 225 cubic feet × 7.48 gallons per cubic foot
So, the volume of the pool in gallons is:
- Volume in Gallons = 225 × 7.48 = 1683 gallons
### Step 3: Calculate the Time Needed to Fill the Pool
Now, we need to calculate the time required to fill the pool. The hose dispenses water at a rate of 10.5 gallons per minute. Using this rate, we can find the time needed to fill the pool by dividing the total volume of the pool by the rate of the hose:
- Time in Minutes = Volume in Gallons / Hose Rate in Gallons per Minute
- Time in Minutes = 1683 gallons / 10.5 gallons per minute
So, the time needed in minutes is:
- Time in Minutes = 1683 / 10.5 ≈ 160.29 minutes
### Step 4: Convert Time to Hours
Finally, we need to convert the time from minutes to hours and round to the nearest hour. There are 60 minutes in one hour:
- Time in Hours = Time in Minutes / 60
- Time in Hours = 160.29 minutes / 60 minutes per hour ≈ 2.67 hours
Rounding 2.67 hours to the nearest whole number, we get:
- Time in Hours ≈ 3 hours
So, it will take approximately 3 hours to fill the pool 6 inches from the top using a garden hose that dispenses water at a rate of 10.5 gallons per minute.
