Question

a street on a hill slopes upward evenly such that the street rises 1 11 foot ( ft ) (ft)(, start text, f, t, end text, )vertically for every 4 ft 4ft4, start text, f, t, end text traveled horizontally. the bottom of the street is 60 ft 60ft60, start text, f, t, end text lower than the top of the street. how long is the street from the bottom to the top in feet?

Answer 1

The length of the street is calculated by setting up a proportion with the given slope rate of 1 foot of rise for every 4 feet of run. With a total vertical rise of 60 feet, the horizontal length of the street is determined to be 240 feet.

Step-by-step explanation:

To solve for the length of the street from the bottom to the top, we need to apply our understanding of similar triangles or the slope of a line.

The question states that the street rises "1 foot vertically" for every "4 feet horizontally."

This gives us a ratio, or a slope, of 1/4. Knowing the total vertical change (the height) is "60 feet," we set up a proportion to find the horizontal distance (the length of the street).

Let x be the length of the street, so our proportion is:

• Vertical rise / Horizontal distance = 1 ft / 4 ft
• 60 ft / x ft = 1 ft / 4 ft

Cross multiplying gives us:

• 1 x = 60 ft × 4 ft
• x = 240 ft

The length of the street from the bottom to the top is 240 feet.