1. The distance, d(t), fallen by a free-falling body is represented by d(t)+vt-0.5gt^2, where v is initial velocity and g is acceleration due to gravity. The acceleration due to gravity is 9.8 m/s^2. If a rock is thrown downward with an initial velocity of 4 m/s from the edge of the North Rim of the Grand Canyon, which is 1750 meters deep, how long will it take the rock to reach the bottom of the Grand Canyon?

2.The length of a rectangular garden is 6ft. more than its width. A path 3ft. wide surrounds the outside of the garden. The total area of the path is 288 square feet. Find the dimensions of the garden.

3. Ron and Mary Beth are hired to stock shelves at a supermarket. It takes them 4 hours working together to complete the job. It would take Ron 6 more hours than Mary Beth to do the job alone. If one of them were absent how long would the other one need to complete the job alone?

4.Determine if a rectangular piece of paper with a perimeter of 36 inches can have an area of 81in^2. State the dimensions if it does exist.

2 answers

#1 -4t-4.9t^2 = -1750
#2 (w+2*3)((w+6)+2*3)-(w)(w+6) = 288
#3 If Mary Beth takes x hours,
1/x + 1/(x+6) = 1/4
#4 clearly a 9x9 square fits the bill
Since a square has maximum area for a given perimeter, no other rectangle can do the job.
Thank you so much for all the help!