Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st St. and Edison Avenue. Her house is at the corner of 42nd St. and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st St., or she can walk through the park. The distance from 42nd St. to 41st St. 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 St. and Edison Avenue. Her house is at the corner of 42nd St. and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st St., or she can walk through the park. The distance from 42nd St. to 41st St. 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 find the distance Sylvia would have to walk if she goes through the park, we need to find the hypotenuse of the right triangle formed by walking through the park.

Using the Pythagorean Theorem, we can calculate the length of the hypotenuse:
a^2 + b^2 = c^2
(80)^2 + (60)^2 = c^2
6400 + 3600 = c^2
10000 = c^2
c = √10000
c = 100 yards

So, if Sylvia walks through the park, she will have to walk 100 yards.

The total distance she would have to walk if she goes straight down Johnson Avenue and turns right on 41st St. is the sum of the two legs of the right triangle:
80 + 60 = 140 yards

Therefore, Sylvia would walk 140 yards if she goes straight down Johnson Avenue and turns right on 41st St. Since it's 100 yards if she goes through the park, she would walk 40 yards less if she goes through the park.