The rate of change in the number of miles of road cleared per hour by a snowplow is inversely proportional to the depth of the snow. Given that 22 miles per hour are cleared when the depth of the snow is 2.3 inches and 13 miles per hour are cleared when the depth of the snow is 9 inches, then how many miles of road will be cleared each hour when the depth of the snow is 11 inches? (Round your answer to three decimal places.) The rate of change in the number of miles of road cleared per hour by a snowplow is inversely proportional to the depth of the snow. Given that 22 miles per hour are cleared when the depth of the snow is 2.3 inches and 13 miles per hour are cleared when the depth of the snow is 9 inches, then how many miles of road will be cleared each hour when the depth of the snow is 11 inches? (Round your answer to three decimal places.)

The number of miles of road that will be cleared each hour when the depth of the snow is 11 inches as is 3.923 miles.

Step-by-step explanation:

Let X = number of miles of road cleared and h = depth of the snowfall.

Then the rat of change in the number of miles of road cleared per hour is given by the differential equation:

Simplify and integrate the above differential equation as follows:

It is provided that:

X (2.3) = 21

X (9) = 13

Use these information to compute the value of k and c as follows:

Now substitute the value of k to compute c as follows:

The equation of X is:

X = -10.912 ln (h) + 30.089

Compute the number of miles of road that will be cleared each hour when the depth of the snow is 11 inches as follows:

Thus, the number of miles of road that will be cleared each hour when the depth of the snow is 11 inches as is 3.923 miles.

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step-by-step explanation: