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?(1 point)

Question

Responses

{y=10+5xy=10+3x
enlarged left brace start layout first row y equals 10 plus 5 x second row y equals 10 plus 3 x end layout

{y=5x−10y=3x −10
enlarged left brace start layout first row y equals 5 x minus 10 second row y equals 3 x minus 10 end layout

{y=−5xy=−3x
enlarged left brace start layout first row y equals negative 5 x second row y equals negative 3 x end layout

{y=10−5xy=10−3x
enlarged left brace start layout first row y equals 10 minus 5 x second row y equals 10 minus 3 x end layout

Answer 1

To model the situation described, we need to establish a relationship between the height of the egg (y) at a time (x) for both parachute designs.

Both eggs are dropped from a height of 10 feet, so at time \( x = 0 \), the height \( y \) is 10 feet. As they fall, their heights decrease with time at their respective rates.

1. For the first design (falling at 5 feet per second):

   • The height decreases by 5 feet for each second that passes. Hence, the equation can be expressed as: \[ y = 10 - 5x \]

2. For the second design (falling at 3 feet per second):

   • The height decreases by 3 feet for each second that passes. So the equation becomes: \[ y = 10 - 3x \]

Combining both equations, we get the system of equations:

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

This matches the option:

{y=10−5xy=10−3x}

This is the correct representation of the situation described.