Answer:
5.6 miles
Step-by-step explanation:
From the question, we can infer that this is an inversely proportionality question.
Let us represent Miles per hour = N
Depth of snow = s
Where k is proportionality constant.
dN/ds = k/s
dN = ds .k/s
Integrating this
∫dN = ∫k/s ds
N = k In s + C
Step 1
We find k
From the question, we are told that:
Given that 20 miles per hour are cleared when the depth of the snow is 2.5 inches
11 miles per hour are cleared when the depth of the snow is 7 inches,
20 = k ln 2.5 + C ..... Equation 1
11 = k ln 7 + C...... Equation 2
11 = k ln 7 + 20 - k ln 2.5
Collect like terms
k ln 2.5 - k ln 7 = 20 - 11
k( In 2.5 - In 7) = 9
k = 9/( In 2.5 - In 7)
k = 9/ -1.0296194172
k = -8.7410938932
Step 2
We find C
20 = k ln 2.5 + C ..... Equation 1
C = 20 - k ln 2.5
C = 20 -(-8.7410938932 In 2.5)
C = 20 + 8.7410938932 In 2.5
C = 20 + 8.0093833208
C = 28.0093833208
Step 3
how many miles of road will be cleared each hour when the depth of the snow is 13 inches
N = k In s + C
= -8.7410938932 ln 13 + 28.0093833208
= -22.420463165 + 28.0093833208
= 5.5889201559
Approximately= 5.6 miles
Therefore, 5.6 miles of road will be cleared each hour when the depth of the snow is 13 inches.
