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?

Answer 1

To find how many blocks Joel would ride in total when biking back to his starting point, we first determine the distance he traveled to his starting point.

1. **Distance Joel biked away from his starting point**:
- He biked 9 blocks East.
- He also biked 12 blocks North.

We can visualize his journey as a right triangle where:
- The horizontal leg (East) is 9 blocks.
- The vertical leg (North) is 12 blocks.

2. **Using the Pythagorean theorem**:
To find the direct distance (the hypotenuse) back to his starting point, we can use the Pythagorean theorem:

\[
c = \sqrt{a^2 + b^2}
\]

Here, \( a = 9 \) blocks (East) and \( b = 12 \) blocks (North).

\[
c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15
\]

So, the direct distance back to his starting point is 15 blocks.

3. **Total distance he rode**:
- Distance away from the starting point = 9 blocks (East) + 12 blocks (North) = 21 blocks.
- Distance back to the starting point = 15 blocks.

Therefore, the total distance he rode:

\[
\text{Total distance} = 21 \text{ blocks (out)} + 15 \text{ blocks (back)} = 36 \text{ blocks}.
\]

So, the total number of blocks Joel would ride all together is **36 blocks**.