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.