Joey, Walt East 4 15 2/3 m from home then he walked west four 21 3/4 meters how far what is Joey from home?
To find how far Joey is from home, we can subtract the distance he walked west from the distance he walked east.
Distance walked east: 4 15 2/3 meters
Distance walked west: 4 21 3/4 meters
First, let's convert the mixed numbers to improper fractions.
Distance walked east: 4 + 15/3 = 4 + 5 = 9
Distance walked west: 4 + 21/4 = 4 + 5.25 = 9.25
Now, let's subtract the distance walked west from the distance walked east.
9 - 9.25 = -0.25
Joey is -0.25 meters from home. This means he started walking 0.25 meters west of his home.
To find out how far Joey is from home, we need to calculate the total displacement caused by his movements. We can break down the steps as follows:
Step 1: Calculate the total distance covered in the east direction.
Joey walked 4 15 2/3 meters to the east. To convert the mixed number into an improper fraction, we have 4 + 15/3 = 4 + 5 = 9/3 + 5/3 = 14/3.
So, Joey walked 14/3 meters to the east.
Step 2: Calculate the total distance covered in the west direction.
Joey walked 4 21 3/4 meters to the west. Again, converting the mixed number into an improper fraction, we have 4 + 21/4 = 4 + 5 1/4 = 4 + 5 + 1/4 = 9 + 1/4 = 10 + 1/4 = 41/4.
So, Joey walked 41/4 meters to the west.
Step 3: Calculate the total displacement.
Since the directions are opposite, we need to subtract the distance covered in the west direction from the distance covered in the east direction.
Total displacement = 14/3 - 41/4
To subtract the fractions, we need to find a common denominator, which is 12 in this case.
Total displacement = (14/3 * 4/4) - (41/4 * 3/3)
= 56/12 - 123/12
= -67/12
The total displacement is -67/12 meters.
Step 4: Find the absolute value of the displacement.
Since displacement is a vector quantity, to determine the magnitude or distance from a point, we need to take the absolute value of the displacement.
Absolute value of -67/12 = 67/12.
Therefore, Joey is 67/12 meters from home.