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

Question

1. y=10 + 5x
y=10+ 3x
2. y= 5x-10
y=3x-10
3. y= 10-5x
y=10 - 3x
4. y=-5x
y=-3x

Answer 1

To represent the situation described in the egg-drop project, we want to establish equations that show how the height \( y \) of the egg decreases over time \( x \) as the egg falls.

The initial height of the egg is 10 feet, and the egg falls at different rates for the two designs.

1. For the first design, the egg falls at a rate of 5 feet per second:

   • The height \( y \) decreases from 10 feet at a rate of 5 feet per second, so the equation is \[ y = 10 - 5x. \]

2. For the second design, the egg falls at a rate of 3 feet per second:

   • Similarly, the height \( y \) also decreases from 10 feet at a rate of 3 feet per second, resulting in the equation \[ y = 10 - 3x. \]

The correct system of equations that represents this situation is:

3. \( y = 10 - 5x \)
\( y = 10 - 3x \)

So the answer is option 3.