Question

Quinton typically walks 28 yards south on Pine Street and 45 yards east on Maple Avenue in order to get to school. How much shorter would his walk be if he took the shortcut shown below.

Shortcut
Pine St.
Maple Ave.
1. How far did he walk south?
2. How far did he walk east?
3. How far is the shortcut?
4. How much shorter would his walk be?

Answer 1

Quinton typically walks 28 yards south on Pine Street and 45 yards east on Maple Avenue. The shortcut is a straight line between these two streets. Using the Pythagorean theorem, the length of the shortcut is approximately 53 yards. Taking the original distance and subtracting the length of the shortcut, Quinton's walk would be 20 yards shorter.

Step-by-step explanation:

To find the answer, let's break down the problem into smaller parts:

1. Quinton walks 28 yards south on Pine Street.
2. Quinton walks 45 yards east on Maple Avenue.
3. The shortcut is shown to be a straight line between these two streets.
4. To find the distance of the shortcut, we can use the Pythagorean theorem: c^2 = a^2 + b^2.
5. After substituting the values, we have c^2 = (28^2) + (45^2).
6. Calculating this, we get c^2 = 784 + 2025.
7. Adding these numbers, we find c^2 = 2809.
8. Taking the square root of both sides, we get c = 53.

The shortcut is approximately 53 yards long.

To find how much shorter Quinton's walk would be, we subtract the length of the shortcut from the original distance: (28 + 45) - 53 = 73 - 53 = 20.

The shortcut would make his walk 20 yards shorter.