All our streets run north-south or east-west, and the shop is 6 blocks east and 8 blocks north.I lost both races.The first tim, i rode directly east for 6 blocks and then directly north for 8 blocks.the next time i tried zig-zagging.both times he was laughing when i got there can you tell how many blocks he beat me by? prove your answer by trying different equations

You have provided no information on the speed of the other bike rider except that he beat you.

Your total distance covered in the zig-zag route is the same as in the east-and-then-north route.

More info is needed to answer your question.

he rides the bike in the same speed

To determine how many blocks the person beat you by, we can use the concept of the Pythagorean theorem. According to the problem, the shop is 6 blocks east and 8 blocks north from your starting point.

In the first case, where you rode directly east for 6 blocks and then directly north for 8 blocks, you can calculate the distance using the Pythagorean theorem:

Distance = √(6^2 + 8^2)
= √(36 + 64)
= √100
= 10 blocks

In the second case, where you zig-zagged, we need to consider the path you took. Since you didn't provide more details about the zig-zagging, let's consider two possible scenarios.

Scenario 1 - Zig-zag moving four blocks east and four blocks north:
In this case, you would travel a total distance of 6 + 4 + 4 = 14 blocks diagonally.

Distance = √(6^2 + 4^2)
= √(36 + 16)
= √52
≈ 7.211 blocks

Scenario 2 - Zig-zag moving three blocks east and five blocks north:
In this case, you would travel a total distance of 6 + 3 + 5 = 14 blocks diagonally.

Distance = √(6^2 + 5^2)
= √(36 + 25)
= √61
≈ 7.810 blocks

Regardless of the zig-zag path taken, both scenarios show that you would have traveled a greater distance than 10 blocks. Therefore, in both cases, the person beat you by a minimum of 10 blocks.

Please note that the distance calculations assume that blocks in the grid are considered as right-angled triangles.