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?
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.
To find the farthest distance she can end up from her friend's house, we need to consider the different possibilities in each direction.
Let's assume her friend's house is at the starting point (0,0) on a coordinate grid.
First, she can walk 3 blocks in any direction from school. This means she can walk 3 blocks east, west, north, or south.
Second, after taking the first turn, she walks 2 blocks. This means she moves an additional 2 blocks in any direction.
Finally, she walks 1 block further, which means she moves an additional 1 block in any direction.
We can calculate the farthest distance using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the three sides of the triangle represent the number of blocks she walks in the east-west direction, the north-south direction, and the distance from her friend's house.
Considering all possible combinations, let's calculate the distance for each:
1. East + North + East: (3 + 2 + 1) blocks east, (3 + 0 + 0) blocks north.
Distance = √((6/8)^2 + (3/8)^2) = √(36/64 + 9/64) = √(45/64) ≈ 0.841 miles
2. East + South + East: (3 + 2 + 1) blocks east, (0 - 3 - 0) blocks north.
Distance = √((6/8)^2 + (-3/8)^2) = √(36/64 + 9/64) = √(45/64) ≈ 0.841 miles
3. West + North + West: (0 - 2 - 1) blocks east, (3 + 0 + 0) blocks north.
Distance = √((-3/8)^2 + (3/8)^2) = √(9/64 + 9/64) = √(18/64) ≈ 0.671 miles
4. West + South + West: (0 - 2 - 1) blocks east, (0 - 3 - 0) blocks north.
Distance = √((-3/8)^2 + (-3/8)^2) = √(9/64 + 9/64) = √(18/64) ≈ 0.671 miles
By considering all possible combinations, we find that the farthest distance she can end up from her friend's house is approximately 0.841 miles.