joe walked 4 miles north, 9 miles east then 8 miles north and 7 miles east if Al decides to walk straight back to where he started how far must he walk?
He walked a total of 12 miles north and 16 miles east.
The Pythagorean Theorem will show the distance of the diagonal back to where he started.
12^2 + 16^2 = c^2
Solve for c.
20miles
To find out how far Al must walk to get back to where he started, we will need to calculate the total distance he walked in each direction and then sum them up.
First, let's analyze Joe's movements. Joe walked 4 miles north, 9 miles east, 8 miles north, and 7 miles east.
To determine how far Al must walk to get back to his starting point, we need to consider that moving north and south cancel each other out, as do moving east and west. This is because when you walk north and then south, the net distance you have traveled in the north-south direction is zero. The same applies to east and west.
So, we can simplify Joe's movements by canceling out the north-south and east-west directions:
Joe moved 4 miles north and then 8 miles north, which gives us a total distance of 4 + 8 = 12 miles traveled north.
Joe moved 9 miles east and then 7 miles east, which gives us a total distance of 9 + 7 = 16 miles traveled east.
Now, we need to find the net north-south and east-west distances Al must walk to get back to his starting point. The net north-south distance is the total north distance minus the total south distance. Similarly, the net east-west distance is the total east distance minus the total west distance.
In this case, Al walked 12 miles north and did not walk south, so the net north-south distance is 12 - 0 = 12 miles.
Al walked 16 miles east and did not walk west, so the net east-west distance is 16 - 0 = 16 miles.
Now that we have the net north-south distance of 12 miles and the net east-west distance of 16 miles, we can calculate the total distance Al must walk using the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse (in this case, the distance Al must walk) is equal to the sum of the squares of the other two sides (north-south and east-west distances).
Using the Pythagorean theorem:
Distance Al must walk = sqrt((12^2) + (16^2)) = sqrt(144 + 256) = sqrt(400) = 20 miles.
Therefore, Al must walk a total distance of 20 miles to get back to where he started.