The area at the bottom of the pool floor is 20 meters squared and the pool is 1.5 meters deep. The hose is filling up the pool at a rate of 50 Liters per minute. How long will it take to fill the pool?
20m^2 * 1.5m * 1000L/m^3
---------------------------- = 600 min
50 L/min
To find out how long it will take to fill the pool, we need to calculate the volume of the pool and then divide it by the rate of filling.
First, let's calculate the volume of the pool.
The formula to find the volume of a rectangular prism (which is the shape of the pool) is:
Volume = Length × Width × Height
Given:
- Area at the bottom of the pool floor = 20 m²
- Depth of the pool = 1.5 meters
To calculate the volume, we need to find the length and width of the pool first. Since only the area is given, we cannot determine the exact length and width. However, assuming the pool is a perfect rectangle, we can say that:
Area = Length × Width
So, we can find the length and width by dividing the given area by either the length or the width.
Let's assume the length of the pool is 4 meters and the width is 5 meters. Thus, the area would be:
Area = Length × Width
Area = 4 meters × 5 meters
Area = 20 meters²
Now that we have the length, width, and depth values, we can calculate the volume:
Volume = Length × Width × Height
Volume = 4 meters × 5 meters × 1.5 meters
Volume = 30 meters³
Now, we know that the hose is filling up the pool at a rate of 50 liters per minute. To convert liters to cubic meters, we need to divide the liters by 1000 (since 1 cubic meter is equal to 1000 liters):
Rate of filling = 50 liters/minute ÷ 1000
Rate of filling = 0.05 cubic meters/minute
Finally, to find out how long it will take to fill the pool, we divide the volume (30 cubic meters) by the rate of filling (0.05 cubic meters/minute):
Time = Volume / Rate of filling
Time = 30 cubic meters / 0.05 cubic meters/minute
Time = 600 minutes
Therefore, it will take approximately 600 minutes to fill the pool.