Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house is at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk through the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90° angles, how much shorter is it for Sylvia to walk through the park?
(1 point)
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be
yards shorter.
Apologies for the mistake. Let's calculate the correct answer.
If Sylvia walks straight down Johnson Avenue and then turns right on 41st Street, the total distance she needs to walk is the sum of the distance from her house to 41st Street and the distance from 41st Street to the bank.
The distance from her house at the corner of 42nd Street to 41st Street is given as 80 yards.
The distance from 41st Street to the bank at the corner of Edison Avenue is given as 60 yards.
Therefore, the total distance of this route is 80 + 60 = <<80+60=140>>140 yards.
If Sylvia chooses to walk through the park, the distance she needs to walk is the direct distance from her house to the bank.
This distance can be found using the Pythagorean theorem, as the distance from 42nd Street to 41st Street is one side of a right triangle and the distance from 41st Street to the bank is another side. The direct distance is the hypotenuse of this right triangle.
Using the given distances, we can calculate the direct distance as:
direct_distance = √(80^2 + 60^2) = √(6400 + 3600) = √10000 = 100 yards.
Therefore, if Sylvia walks through the park, the walk will be 140 - 100 = <<140-100=40>>40 yards shorter.
Answer: 40 yards shorter.
If Sylvia walks through the park, she needs to walk from 42nd Street to the intersection of 41st Street and Edison Avenue.
This can be broken down into two steps:
1) Walking from 42nd Street to the intersection of 42nd Street and Johnson Avenue, which is 80 yards.
2) Walking from the intersection of 42nd Street and Johnson Avenue to the intersection of 41st Street and Edison Avenue, which is 60 yards.
The total distance through the park is 80 + 60 = <<80+60=140>>140 yards.
If Sylvia walks straight down Johnson Avenue and then straight down 41st Street, she only needs to walk from 42nd Street to the intersection of 41st Street and Edison Avenue. This distance is 60 yards, as given.
Therefore, the walk through the park is 140 - 60 = <<140-60=80>>80 yards shorter than walking straight down Johnson Avenue and then straight down 41st Street. Answer: \boxed{80}.
nope
To determine how much shorter it is for Sylvia to walk through the park, we need to calculate the total distance of both routes and then compare them.
First, let's calculate the distance of walking straight down Johnson Avenue and turning right on 41st Street:
- The distance from 42nd Street to 41st Street is 80 yards.
- The distance from Johnson Avenue to Edison Avenue is 60 yards.
So, the total distance for this route is 80 yards + 60 yards = 140 yards.
Now let's calculate the distance of walking through the park:
- Sylvia's house is at the corner of 42nd Street and Johnson Avenue.
- The distance from 42nd Street to 41st Street is 80 yards.
- The distance from 41st Street to Edison Avenue is the same as before, which is 60 yards.
So, the total distance for this route is 80 yards + 60 yards = 140 yards.
Since both routes have the same total distance of 140 yards, it means that there is no difference in length between walking straight down Johnson Avenue and turning right on 41st Street, or walking through the park.
Therefore, if Sylvia chooses to walk through the park instead of taking the streets, the walk will not be shorter.