Question

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?

_ blocks

Answer 1

To solve the problem, we first determine the total distance that Joel biked in the first part of his trip:

- He biked 9 blocks East.
- He biked 12 blocks North.

The total distance biked away from the starting point is the sum of these distances:
\[
9 + 12 = 21 \text{ blocks}
\]

Now, we need to find the most direct route back to the starting point. The position after biking 9 blocks East and 12 blocks North can be represented as a point with coordinates (9, 12).

To return to the starting point (0, 0), we need to travel:
- 9 blocks West (opposite of East)
- 12 blocks South (opposite of North)

The distance back is the same as the distance traveled out:
\[
9 + 12 = 21 \text{ blocks}
\]

Now we total all the blocks biked (both out and back):
\[
\text{Total distance} = 21 \text{ blocks (out)} + 21 \text{ blocks (back)} = 42 \text{ blocks}
\]

Thus, the total number of blocks that Joel would ride altogether is:
\[
\boxed{42}
\]