Problem: my neighborhood is full of one-way streets. to drive from my house to the grocery store, i have to go 1 block south, then 1 block east, then 5 blocks north, then 2 blocks east. each block is $\frac{1}{16}$ of a mile. how much shorter would my trip be if i could fly like a bird?

This problem is actually very simple. The first step would be to figure out the number of blocks he/she (I''ll call the person Bob) drove total. If Bob drove 1 block south, then 1 block east, then 5 blocks north, then 2 blocks east, we want the total so we add everything together. We would solve 1+1+5+2 and get 9. This means that Bob drove 9 blocks. Since we want our answer in miles, we would do 9 ( blocks walked )*1/16( length of each block ) to get 9/16 miles driven. We cannot simplify this fraction.

Now, let's figure where the grocery store is. I used a coordinate plane for this. If Bob's house is at (0,0), 1 block south would be at (0.-1). Next, we travel 5 blocks north. This would be at (1, 4). Finally, Bob drives 2 blocks east. He would now be at the grocery store, (3,4). Now, we know that Bob's house is at (0,0) and the grocery store is at (3,4).

Now, let's start the last step- finding the distance of Bob's house to the grocery store if he traveled in a straight line. To do this, we would first need to find the slope of the line. This would be 4/3 since Bob can drive 4 blocks up/down and 3 blocks left/right to get to each point on the coordinate plane. Now we know the slope. How do we find the distance of Bob's house to the grocery store if he traveled in a straight line? Let's apply our newly learned theorem, ( watch me try to spell it lol ) the Pythagorean Theorem! But how does this apply to the length of a line segment? Well, let's think about line segments not as line segments, but as the hypotenuse of a right triangle! This means that since the slope of the line segment is 4/3, one of the legs of the triangle is 4 and the other leg is 3.

Earlier, we learned that since the slope of the line segment is 4/3, one of the legs of the triangle is 4 and the other leg is 3. Now, let's use this information to find the length of the line segment. We know that one leg is 4 and the other is 3. Let's apply the Pythagorean Theorem. But what is the Pythagorean Theorem? Basically, it is just a law stating that the sum of the 2 legs of a right triangle is equal to the square of the hypotenuse. So, let's square our two legs, 4 and 3. We would get 16 and 9. Once we add these up, we would have 25. Now, we need to find the square root of 25. This is rather simple because 25 is a perfect square, and we would simply get 5.

This means that the length of Bob's trip if he could fly like a bird is 5 blocks. However, we want the answer in miles. Since 5*1/16 is 5/16, 5 blocks is equal to 5/16 of a mile. This is the distance between Bob's house and the grocery store if he were to fly in a straight line. Finally, we want to know how much shorter Bob's trip would be. We would simply subtract 5/16 from 9/16 to get 4/16. Or, simplified, 1/4 of a mile.