Direct vs. Indirect Variation
The volume of the water in a swimming pool as it is filled at a rate of 200 gallons per minute.
I said this is direct variation V = 200t
The volume of the water in a swimming pool as the water drains at a rate of 200 gallons per minute.
I believe that this would also be direct variation?? Such as V = -200t?
But the answer packet says it is neither direct nor inverse variation.
no
V = F - 200 t
Where F is the full volume
To understand why the answer packet states that the volume of the water in a swimming pool as it drains at a rate of 200 gallons per minute is neither direct nor inverse variation, let's first discuss what direct and inverse variation mean.
Direct variation occurs when two variables change proportionally, meaning that as one variable increases (or decreases), the other variable also increases (or decreases) by the same factor. In this case, if the volume of water in the pool changes directly with time, we would expect the volume to increase at a constant rate of 200 gallons per minute.
Inverse variation occurs when two variables change inversely, meaning that as one variable increases, the other variable decreases by the same factor, and vice versa. In other words, as one variable gets larger, the other variable gets smaller at a constant rate. In this case, if the volume of water in the pool changes inversely with time, we would expect the volume to decrease at a constant rate of 200 gallons per minute.
However, in the case of draining a swimming pool, the volume of water decreases over time. The relationship between the volume of the water and time is not directly proportional because as time increases, the volume of water decreases, not increases. Additionally, it is not inversely proportional either because as time increases, the volume of water decreases but not at a constant rate.
In this scenario, the rate at which the volume of water decreases depends on the size of the pool and the initial volume of water in it. Therefore, the relationship between the volume of water and time while draining does not fit into either the direct or inverse variation category mentioned earlier.