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 80yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90 degree angles, how much shorter is it for Sylvia to walk through the park?

Question

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 80yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90 degree angles, how much shorter is it for Sylvia to walk through the park?

If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st street, the walk will be how many yards shorter.

Answer 1

To calculate the distance Sylvia saves by walking through the park, we need to calculate the distance of both routes.

Through Johnson Avenue and 41st Street:
Distance from 42nd street to 41st street: 80 yards
Distance from Johnson Avenue to Edison Avenue: 60 yards
Total distance: 80 + 60 = 140 yards

Through the park:
Distance from 42nd street to 41st street is a straight line, forming the hypotenuse of a right triangle.
The length of this hypotenuse can be found with the Pythagorean theorem:

c^2 = a^2 + b^2

In this case, a = 80 yards and b = 60 yards.
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000

Solving for c:
c = √10000
c = 100 yards

Therefore, by walking through the park, Sylvia walks a total of 100 yards.

The difference in distance between the two routes is: 140 - 100 = <<140-100=40>>40 yards.