Question

She doesn't know the exact route to her friends house. She knows that the route is 3 blocks to the first turn, 2 blocks to the second turn and then 1 block further. She can walk east, west or north when she leaves school and the blocks are 1/8 mile long. What is the farthest distance she can end up from her friends house?

Answer 1

we can pick any direction for the 1st 3 blocks. Say, North.

After the 1st 3 blocks N, E and W are interchangeable.

Clearly, going N then S will not help, so she can do one of the following:
E for 2, N for 1
E for 2, W for 1
E for 2, S for 1

I think you can tell which gives the greatest distance.

So, starting at (0,0) figure where she ends up, then use the usual distance formula to find out how many blocks that is.

Finally, multiply the above answer by 1/8 mile to find the desired distance.