Two students were testing the parachute designs they made for an egg-drop project. Both students dropped their eggs from a height of 10 feet. One design made the egg fall at a rate 5 feet per second, and the other design made the egg fall at a rate of 3 feet per second. If x represents the time in seconds that the egg falls and y represents the height of the egg, which system of equations represents the situation described?

Answer 1

To model the situation described, we can create equations based on the height of the egg after a certain amount of time has passed.

For the first student's parachute design, the egg falls at a rate of 5 feet per second. Therefore, the height \( y \) of the egg can be expressed as:

\[ y = 10 - 5x \]

For the second student's parachute design, the egg falls at a rate of 3 feet per second. The height \( y \) of the egg for this design can be expressed as:

\[ y = 10 - 3x \]

Now, we can express these two equations together in a system of equations:

1. \( y = 10 - 5x \) (for the first parachute design)
2. \( y = 10 - 3x \) (for the second parachute design)

Thus, the system of equations representing the situation described is:

\[ \begin{align*} y &= 10 - 5x \ y &= 10 - 3x \end{align*} \]