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)
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be ___ yards shorter.

Answer 1

To find out how much shorter it is for Sylvia to walk through the park, we can use the Pythagorean theorem.

The distance walking straight down Johnson Avenue and then straight down 41st Street is the hypotenuse of a right triangle with legs of 80 yards and 60 yards.

Therefore, the distance can be calculated using the formula:
\(c^{2} = a^{2} + b^{2}\)
\(c^{2} = 80^{2} + 60^{2}\)
\(c^{2} = 6400 + 3600\)
\(c^{2} = 10000\)
\(c = 100\)

So, the distance walking straight down Johnson Avenue and then straight down 41st Street is 100 yards.

The distance walking through the park is the hypotenuse of a right triangle with legs of 80 yards and 60 yards.

Therefore, the distance can be calculated using the same formula:
\(c^{2} = a^{2} + b^{2}\)
\(c^{2} = 80^{2} + 60^{2}\)
\(c^{2} = 6400 + 3600\)
\(c^{2} = 10000\)
\(c = 100\)

So, the distance walking through the park is also 100 yards.

Therefore, the difference in distance between walking straight down Johnson Avenue and then straight down 41st Street and walking through the park is 0 yards.

Answer 2

are you sure

Answer 3

Apologies for the mistake in my previous response. Let's try the calculations again.

The distance walking straight down Johnson Avenue and then straight down 41st Street is the hypotenuse of a right triangle with legs of 80 yards and 60 yards.

Using the Pythagorean theorem:
\(c^{2} = a^{2} + b^{2}\)
\(c^{2} = 80^{2} + 60^{2}\)
\(c^{2} = 6400 + 3600\)
\(c^{2} = 10000\)
\(c = 100\)

So, the distance walking straight down Johnson Avenue and then straight down 41st Street is 100 yards.

Now, let's calculate the distance walking through the park. This path forms a right triangle with legs of 80 yards and 60 yards as well.

Using the Pythagorean theorem:
\(c^{2} = a^{2} + b^{2}\)
\(c^{2} = 80^{2} + 60^{2}\)
\(c^{2} = 6400 + 3600\)
\(c^{2} = 10000\)
\(c = 100\)

So, the distance walking through the park is also 100 yards.

Therefore, the difference in distance between walking straight down Johnson Avenue and then straight down 41st Street and walking through the park is 0 yards. The two paths are the same length.