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 determine how much shorter it is for Sylvia to walk through the park, we need to calculate the distance of each route. Route 1: Walking down Johnson Avenue and turning right on 41st Street. Distance = 80 yards + 60 yards = 140 yards Route 2: Walking through the park. This route forms a right triangle with sides of 80 yards and 60 yards. Using the Pythagorean theorem, we can calculate the hypotenuse (c) which is the shortest distance through the park. c^2 = 80^2 + 60^2 c^2 = 6400 + 3600 c^2 = 10000 c = 100 yards Therefore, the distance for Sylvia to walk through the park is 100 yards, which is 40 yards shorter than walking down Johnson Avenue and turning right on 41st Street.