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 to Johnson Avenue and turn right on 41st street, or she can walk through the park. The distance from 42nd 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?

Answer 1

To walk through the park, Sylvia would only need to walk along one side of the right triangle formed by the streets. The two legs of the triangle are 80 yards and 60 yards. To find the hypotenuse, we can use the Pythagorean theorem:

c^2 = a^2 + b^2

where c is the hypotenuse and a and b are the legs of the triangle.

c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000

Taking the square root of both sides, we find:

c = 100 yards

Therefore, the distance Sylvia would need to walk through the park is 100 yards.

To walk through the streets, Sylvia would need to walk 80 yards and then 60 yards, for a total of 80 + 60 = <<80+60=140>>140 yards.

Therefore, by walking through the park, Sylvia would walk 140 - 100 = <<140-100=40>>40 yards less. Answer: \boxed{40}.