Consider the diagram showing the path that Joel biked.

Joel bikes 9 blocks East and 12 blocks North. If he biked back to his starting point using the most direct route, how many blocks would he ride all together?

1 answer

To find the total distance Joel biked, we first need to determine the distance he traveled initially and then the distance he biked back to his starting point.

  1. Distance Biked East and North:

    • Joel biked 9 blocks East and 12 blocks North.
    • Therefore, the total distance for this part of his trip is: \[ 9 \text{ blocks (East)} + 12 \text{ blocks (North)} = 21 \text{ blocks} \]
  2. Distance Biking Back to the Starting Point:

    • To return to the starting point, Joel needs to bike the same distance he traveled but in the opposite direction.
    • Since he originally biked 9 blocks East, he must bike 9 blocks West to return in that direction.
    • Similarly, since he biked 12 blocks North, he must bike 12 blocks South to return in that direction.
    • The distance he travels back is also: \[ 9 \text{ blocks (West)} + 12 \text{ blocks (South)} = 21 \text{ blocks} \]
  3. Total Distance Traveled:

    • Now, we add the total distance traveled in both directions: \[ 21 \text{ blocks (outgoing)} + 21 \text{ blocks (returning)} = 42 \text{ blocks} \]

Thus, the total distance Joel rode altogether is \(\boxed{42}\) blocks.

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