To determine the total distance Joel biked, we need to calculate both the distance he biked away from the starting point and the distance he traveled back to the starting point.
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Distance biked away from the starting point:
- Joel bikes 9 blocks East and 12 blocks North. Therefore, the total distance he biked away from the starting point is: \[ 9 + 12 = 21 \text{ blocks} \]
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Distance to bike back to the starting point:
- To find the most direct route back, we apply the Pythagorean theorem. His position relative to the starting point after biking is represented by a right triangle, where the legs of the triangle are:
- 9 blocks (East direction)
- 12 blocks (North direction)
The distance back to the starting point (the hypotenuse \(d\)) can be calculated as: \[ d = \sqrt{(9^2) + (12^2)} = \sqrt{81 + 144} = \sqrt{225} = 15 \text{ blocks} \]
- To find the most direct route back, we apply the Pythagorean theorem. His position relative to the starting point after biking is represented by a right triangle, where the legs of the triangle are:
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Total distance biked:
- The total bike distance includes both the distance away and the distance back: \[ 21 + 15 = 36 \text{ blocks} \]
Thus, the total number of blocks that Joel rode altogether is 36.