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Answer:
The change in horizontal distance is 1.72 mi
Step-by-step explanation:
From the question, the highway has a 11% grade, which means that its slope is -11 / 100.
The negative sign indicates that the road is descending.
Hence, slope (m) = 11/100
The slope m, is given by
Where Δy is the change in vertical distance and
Δx is the change in horizontal distance
Now, from the question, you have descended a distance of 1000 ft, that is
Δy = 1000 ft
Then, to determine the change in the horizontal distance Δx,
From
, then
∴
Δx = 9090.91 ft
This is the change in horizontal distance in ft, Now to convert it to miles
1 mile = 5280 ft
Hence, 1 ft = 1/5280 miles
If 1 ft = 1/5280 miles
Then, 9090.91 ft = x miles
x = 9090.91 × 1/5280
x = 1.72 miles
Hence, the change in horizontal distance in miles is 1.72 mi