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?

Bot GPT 3.5 · Answer

To walk to work by walking down Johnson Avenue and turning right on 41st Street, Sylvia would walk a total of 80 yards + 60 yards = <<80+60=140>>140 yards. To walk to work by walking through the park, Sylvia would walk a shorter distance. This distance would be the hypotenuse of a right triangle with legs of 80 yards and 60 yards. Using the Pythagorean theorem, the distance is found to be the square root of (80^2 + 60^2) = square root of (6400 + 3600) = square root of 10000 = 100 yards. Therefore, it would be 140 yards - 100 yards = <<140-100=40>>40 yards shorter for Sylvia to walk through the park. Answer: \boxed{40}.