John has to walk to work when the weather is nice he works at the bank at the corner of 41st Street and Edison avenue his house is at the corner of 42nd street and Johnson avenue he can walk down Johnson avenue and turn right on 41st Street or he can walk through the park the distance from 42nd Street to 41st Street is 80 yd and it is 6 years from Johnson avenue to Edison avenue assuming the street intersections are 90 angles how much shorter is it for John to walk through the park
To calculate the difference in distance between walking through the park and taking the streets, we need to find the lengths of each route.
Walking through the streets:
John would walk from 42nd Street to 41st Street, which is a distance of 80 yards.
Then, he would turn right onto 41st Street and walk from there to Edison Avenue, which is a straight line distance.
Since the street intersections are at 90-degree angles, we can use the Pythagorean theorem to calculate the total distance.
Using the Pythagorean theorem:
Let's assume the distance from 42nd Street to Edison Avenue (41st Street) is represented by d.
We know the distance from 42nd Street to 41st Street is 80 yards, and the distance from 41st Street to Edison Avenue is 6 yards.
Using the Pythagorean theorem, we can calculate d:
d^2 = (80^2) + (6^2)
d^2 = 6400 + 36
d^2 = 6436
Taking the square root of both sides to find d:
d ≈ √6436
d ≈ 80.20 yards (rounded to two decimal places)
So, the total distance walking through the streets is approximately 80.20 yards.
Walking through the park:
Since we don't have any specific measurements for walking through the park, we cannot calculate the exact distance.
Therefore, we are unable to determine how much shorter it is for John to walk through the park compared to taking the streets.