Question

The distance traveled by migrating swallows can be represented by y=200x , where y is the distance traveled in miles, and x is the time in days.

Answer 1

The question is about the calculation of distance traveled by migrating swallows using the equation y=200x, representing a direct mathematically proportional relationship between distance and time.

Step-by-step explanation:

The student's question involves the mathematical relationship between distance traveled and time, represented by the equation y=200x. This linear equation suggests the swallow migrates at a constant speed of 200 miles per day. To find the distance the swallow traveled, we multiply its speed by the time spent traveling. This equation reflects a basic principle of motion where speed equals distance divided by time, which can be rearranged to show that distance equals velocity multiplied by time.

For example, if we wanted to calculate how far the swallow traveled in 3 days, we would substitute x with 3:
y = 200 * 3
y = 600 miles.

The migration of animals, such as the Swainson's hawk, that travel thousands of miles is an impressive natural phenomenon and can be analyzed using similar mathematical relationships.

Answer 2

Final Answer:

The distance traveled by migrating swallows after 5 days is 1000 miles.

Step-by-step explanation:

The given equation representing the distance traveled is
`\(y = 200x\),` where
`\(y\)`is the distance in miles, and
`\(x\) i`s the time in days. To find the distance after 5 days, substitute
`\(x = 5\)` into the equation:

`\[ y = 200 * 5 = 1000 \]`

Therefore, after 5 days, the migrating swallows cover a distance of 1000 miles. The coefficient 200 in the equation indicates the rate of travel, meaning that the swallows cover 200 miles each day. Multiplying this rate by the number of days gives the total distance traveled.

In this context, the equation represents a linear relationship between time and distance, with a constant rate of 200 miles per day. This type of linear equation is useful for modeling scenarios where a consistent rate of change is observed over time. The solution, 1000 miles after 5 days, provides a direct and concise answer to the question posed, demonstrating the application of the equation in calculating the distance traveled by the swallows at a specific point in time.