Question

Bethany and her family are attending the Funville Town Fall Festival, and the first thing they do is get in line for the Maize (corn) Maze. When Bethany gets to the entrance of the Maze she is facing north. Following the paths, she walks straight ahead for 10 feet and reaches an intersection at which she turns right and walks 40 feet east, at which point the path dead ends. Bethany decides to back-track 15 feet and turns south. She walks 5 feet south and then turns and walks 6 feet east. If Bethany was to walk straight back to the entrance, cutting through the corn and disregarding the paths, how far would she have to walk? Express your answer as a decimal to the nearest tenth.

Later that day Bethany and her brother Ben decide to go through the Maize Maze again. When Bethany starts she walks 10 feet north, 30 feet west, and then 20 feet north. During this same time, Ben walks 20 feet north, 25 feet east, and then 15 feet south. Disregarding paths, what is the shortest distance between Ben and Bethany? Express your answer to the nearest whole number.



When Bethany’s family is leaving the festival they pick up a flyer, and it says that the Maize Maze is on a square plot of land that is 100 yards by 100 yards. The path through the maze is 1.5 yards wide and 3000 yards long. If one square yard of land holds 18 stalks of corn, how many stalks of corn are in the Maize Maze? Assume that the entire plot of land has corn planted on it except for what is cleared to create the paths.

Answer 1

Part 1: 31.4 feet

Part 2: 61 feet

Part 3: 99,000 stalks of corn

Explanation:

Part 1:

Diagram attached.

You can follow the problem closely and draw a diagram like this. The RED LINE is the distance we are looking to find.

The red line is the hypotenuse of a right triangle we can create (see the dotted line). We can now use the pythagorean theorem to solve for the distance.

Pythagorean Theorem is hypotenuse^2 = leg^2 + leg^2

Let red line [what we want to find] be h and the other 2 sides are 10-5=5 ft & 25 + 6 = 31ft. So we have:

`h^2 = 31^2 + 5^2\\h=√(31^2 + 5^2) \\h=31.4`

Hence Bethany has to walk 31.4 feet

Part 2:

See 2nd diagram attached.

The blue line is the path of Bethany and the green line is path of Ben. The RED line is what we are looking to find, the shortest distance between them.

We use Pythagorean Theorem twice on the two triangles and add up the results.

Left Triangle:

If we make a triangle, we have base (one leg) = 30 and the other leg is 20-10=10. So we have:

`h^2=30^2 + 10^2\\h=√(30^2 + 10^2) \\h=31.62`

RightSide triangle:

two legs are 25 and 15 respectively, so we use the pythagorean theorem again:

`h^2=25^2 + 15^2\\h=√(25^2 + 15^2) \\h=29.15`

Thus, the shortest distance = 31.62 + 29.15 = 60.77 = 61 feet (rounded to nearest whole number)

Part 3:

The area of the Maize MINUS the area of the path is the Area of the Corn [what we are looking for].

Area of Maze:

100 * 100 = 10,000 sq. yd.

Area of Path = 1.5 * 3000 = 4,500 sq. yd.

Area of Corn = 10,000 - 4,500 = 5,500 sq. yard of land.

Now, each sq. yd. holds 18 stalks, so 5,500 sq. yd. will hold:

18 * 5,500 = 99,000 stalks of corn