Short Answer 
The relationship between work and time indicates that as one increases, the other decreases. By establishing two equations for the eating rates of a puppy and a kitten, the solutions reveal that the kitten takes 15 seconds and the puppy takes 10 seconds to eat a sausage, demonstrating their efficient combined rates.
Step 1: Understand the Relationship Between Work and Time
The concept of work and time is based on the principle that the amount of work done is inversely proportional to the time taken to complete it. This means as you increase one, the other decreases. For instance, if multiple entities are working together, their combined rate can be derived from the individual rates.
Step 2: Set Up the Equations
In this scenario, we have two animals: a puppy and a kitten. We let x be the time it takes the puppy to eat a sausage and y for the kitten. Based on their eating rates, we can establish two equations:
- ( frac{1}{x} + frac{1}{y} = frac{1}{6} )
- ( frac{1}{x} – frac{1}{y} = frac{1}{5} )
Step 3: Solve the Equations
To find the time it takes for each animal to eat a sausage, substitute one equation into the other. Begin with the second equation to express x in terms of y, then plug this back into the first equation. After simplifying, you will find that the kitten takes 15 seconds and the puppy takes 10 seconds. Therefore, their consumption rates effectively allow them to work together more efficiently.