Scenario 1 is a direct variation. As the time to make pancakes increases (from 2 to 5 minutes), the number of pancakes made also increases (from 10 to 25).
Scenario 2 is an inverse variation. When Robert and Tiffany work together, they take half the time (25 minutes) compared to Robert working alone (50 minutes), indicating an inverse relationship between the number of people and time taken.
A direct variation occurs when two quantities change in the same direction. In Scenario 1, both the time and the number of pancakes made increase simultaneously, confirming a direct variation. As Maria spends more time, she can naturally make more pancakes.
An inverse variation, on the other hand, describes two quantities changing in opposite directions. In Scenario 2, the number of people working (Robert and Tiffany) increases, but the time taken to cut the grass decreases. This demonstrates an inverse relationship, where increased workforce leads to reduced time spent.
To distinguish between these types of variations, consider the following:
- Direct variation: If one quantity increases, the other quantity also increases, or vice versa. You can imagine a straight line with a positive slope when graphing this relationship.
- Inverse variation: If one quantity increases, the other quantity decreases, and vice versa. The graph of this relationship would be a curve with a negative slope.