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. check answer remaining attempts 3

Explanation:

Step1: Calculate the distance of walking down the streets

The distance of walking down Johnson Avenue and 41st Street is the sum of the two distances. Let \(a = 80\) yards (distance between streets) and \(b=60\) yards (distance between avenues). The distance \(d_1=a + b\).

$$d_1=80 + 60=140$$

Step2: Calculate the distance of walking through the park

Since the street intersections are \(90^{\circ}\) angles, we can use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) (where \(c\) is the distance through the park). Substitute \(a = 80\) and \(b = 60\) into the formula:

$$c=\sqrt{80^{2}+60^{2}}=\sqrt{6400 + 3600}=\sqrt{10000}=100$$

Step3: Calculate the difference in distances

The difference \(\Delta d=d_1 - c\). Substitute \(d_1 = 140\) and \(c = 100\) into the formula:

$$\Delta d=140-100 = 40$$

Answer:

40