Applications of Quadratic Equations Test

Mary owns a small sailboat that is currently being pulled into a dock. To accomplish this task, she has attached a rope from the top of the dock to the boat at water level. When she pulls the boat to a distance of 12 feet away from the dock, the length of the rope from the boat to the dock is 3 feet longer than twice the height of the dock. Find the height of Mary's dock.

Two cars left an intersection at the same time. One of the cars traveled directly north, while the other car traveled directly west. Four hours later, they ended up being exactly 200 miles apart from each other. If the car that traveled north had gone 40 miles farther than the car headed west, how far did each car travel?

The length of a rectangular garden is 10 feet more than the width. If the area of the garden is 600 square feet, what are the dimensions of the garden? Note: (Area is length times width)

A toy rocket is launched vertically upward from an initial height of 33 feet. The initial velocity is 82 feet per second. Find out how long before the rocket will hit the ground. Note: (We will disregard air resistance)
Formula: $$h=-16t^2 + v_{0}t + s_{0}$$ v₀ is the initial velocity in feet per second
s₀ is the initial height in feet the projectile is launched from
t is the number of seconds

Joan wants to buy a rug for her office which measures 15 feet wide by 20 feet long. She doesn't want the rug to cover the entire room. She wants to leave an even strip of flooring, which is uncovered around the edges of the room. If she purchases a rug with an area of 234 square feet, what is the width of the even strip of uncovered floor?