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?

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 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)

GPT 3.5 · Answer

By walking down Johnson Avenue and turning right on 41st Street, Sylvia would need to walk 80 yards + 60 yards = <<80+60=140>>140 yards.
The distance of the hypotenuse walking through the park can be found using the Pythagorean theorem, with one side being 80 yards and the other side being 60 yards.
The square of the hypotenuse is equal to (80 yards)² + (60 yards)² = 6400 yards² + 3600 yards² = 10000 yards².
Therefore, the hypotenuse is sqrt(10000 yards²) = <<sqrt(10000)=100>>100 yards.
Therefore, Sylvia can walk a total of 100 yards - 140 yards = <<100-140=-40>>-40 yards shorter by walking through the park. Answer: \boxed{-40}.