Jimmy ran 3 miles west from home and then turned north and jogged 4 miles. In a straight line, how far is Jimmy from home?
A 3.5 miles
B 4 miles
C 5 miles
D 7 miles
E 17 miles
Distance from Home After Jogging 3 Miles West and 4 Miles North
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The correct answer is C 5 miles.
To find out how far Jimmy is from home after running, we can use the Pythagorean theorem.
1. He ran 3 miles west and then 4 miles north. We can think of these two paths as the two legs of a right triangle.
2. The formula for the Pythagorean theorem is: ( a^2 + b^2 = c^2 ), where ( c ) is the hypotenuse (the straight-line distance from home).
3. Here, ( a = 3 ) miles and ( b = 4 ) miles.
4. So, we calculate: ( 3^2 + 4^2 = c^2 ) which gives ( 9 + 16 = c^2 ), or ( 25 = c^2 ).
5. Taking the square root of both sides, we find that ( c = 5 ) miles.
Therefore, Jimmy is 5 miles away from home.