So you like to walk to work on the weather is nice. She works at the bank at the corner 41st St. and Edison Avenue. Her house is at the corner of 42nd St. and Johnson Avenue. She can walk down Johnson Avenue and turn right onto 41st St. she can walk through the park distance from 42nd St. to 41st St. is 80 yard 60 yards and Johnson Ave., Edson Avenue the street intersections are 90° angles how much shorter is it for so walk-through the park. Sylvia walks through the park instead of straight down Johnson Avenue straight down 41st St., the walk will be blank shorter
The walk through the park will be 100 yards shorter.
To calculate the difference in distance, we need to find the lengths of both routes.
1. Straight down Johnson Avenue:
Distance from Sylvia's house to the corner of Johnson Avenue and 41st St. = 1 block = 80 yards
Distance from the corner of Johnson Avenue and 41st St. to the corner of Edison Avenue and 41st St. = 1 block = 60 yards
Total distance = 80 yards + 60 yards = 140 yards
2. Through the park:
Distance from Sylvia's house to the corner of 42nd St. and 41st St. = 1 block = 80 yards
Distance from the corner of 42nd St. and 41st St. to the corner of Edison Avenue and 41st St. (walking through the park) = 60 yards
Total distance = 80 yards + 60 yards = 140 yards
The lengths are equal, so the walk through the park is 140 yards - 140 yards = 0 yards shorter.
To calculate how much shorter the walk is by going through the park instead of straight down Johnson Avenue and then straight down 41st St., we need to find the total distance of both routes and compare them.
1. Straight down Johnson Avenue and then straight down 41st St.:
- Distance from Sylvia's house to the corner of Johnson Avenue and 41st St. = 80 yards
- Distance from there to the bank at the corner of 41st St. and Edison Avenue = 60 yards
- Total distance = 80 yards + 60 yards = 140 yards
2. Through the park:
- Distance from Sylvia's house to the corner of 42nd St. and Johnson Avenue = 90 yards
- Distance from there to the bank at the corner of 41st St. and Edison Avenue = 60 yards
- Total distance = 90 yards + 60 yards = 150 yards
The walk through the park is 150 yards long, and the straight route is 140 yards long.
Therefore, the walk through the park is 10 yards shorter than going straight down Johnson Avenue and then straight down 41st St.
To answer the question, we need to calculate the difference in distance between walking through the park and walking straight down Johnson Avenue and then turning right onto 41st St.
First, let's find the total distance of walking straight down Johnson Avenue and turning right onto 41st St. We know that the distance from Sylvia's house at the corner of 42nd St. and Johnson Avenue to the intersection of 42nd St. and 41st St. is 80 yards. Since the street intersections are at 90° angles, we can consider this distance as the hypotenuse of a right triangle.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the remaining side of the right triangle, which represents the distance of walking straight down 41st St.
Let's label the remaining side as "d". The known side lengths are:
- The side adjacent to the angle (80 yards)
- The side opposite to the angle (60 yards)
By substituting these values into the Pythagorean theorem and solving for "d", we can find the distance of walking straight down 41st St.
80^2 + 60^2 = d^2
6400 + 3600 = d^2
10000 = d^2
d = √10000
d = 100 yards
Therefore, the distance of walking straight down Johnson Avenue and turning right onto 41st St. is 100 yards.
Now let's find the distance of walking through the park. We know that the distance from the intersection of 42nd St. and Johnson Avenue to the intersection of 42nd St. and Edison Avenue (corner of the bank) is 90 yards. Therefore, the distance of walking through the park is 90 yards.
To calculate how much shorter it is to walk through the park, we subtract the distance of walking through the park from the distance of walking straight down Johnson Avenue and turning right onto 41st St.
100 yards - 90 yards = 10 yards
So, it is 10 yards shorter to walk through the park instead of straight down Johnson Avenue and turning right onto 41st St.