Question

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?

A: { y = 10 + 5x
{ y = 10 + 3x

B: { y = 5x - 10
{ y = 3x - 10

C: {y = 10 - 5x
{ y = 10 - 3x

D: { y = -5x
{ y = -3x

Answer 1

To represent the situation described, we need to formulate an equation for the height of the egg as it falls over time. The height starts at 10 feet and decreases as the egg falls.

1. For the first design, the egg falls at a rate of 5 feet per second. The equation for the height \( y \) of the egg after \( x \) seconds can be formulated as:
\[
y = 10 - 5x
\]
This equation shows that as \( x \) (time) increases, \( y \) (height) decreases.

2. For the second design, the egg falls at a rate of 3 feet per second. The equation for this egg's height can be formulated as:
\[
y = 10 - 3x
\]
Similar to the first, this equation also reflects a decrease in height as time increases.

Combining both equations, the system can be represented as:
\[
\{ y = 10 - 5x
\{ y = 10 - 3x
\]

Based on the options provided, the correct answer is:

**C:**
\[
\{ y = 10 - 5x
\{ y = 10 - 3x
\]