# A snowstorm dumped 18 inches of snow in 12 hours. How many inches of snow fell in 1 hour?

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Hint: Assume the rate of dumping of snow to be x inches per hour. Create an equation from the above statement and solve for x. The value of x will be the number of inches of snow falling in 1 hour.

Complete step-by-step answer:

The above question can be solved by assuming that the rate of falling of snow is constant and uniform over time. This assumption is important for us to be able to solve the question.

Let us assume that the rate of falling of snow is x inches per hour.

Since the rate is uniform, the amount of snow dumped in 12 hours = 12x.

But according to the question, the amount of snow dumped in 12 hours = 18.

So, we have 12x = 18

Dividing both sides by 12, we get

$\dfrac{12x}{12}=\dfrac{18}{12}$

i.e. x = $\dfrac{3}{2}inch/hr$

Hence the amount of snow which fell in 1 hour $=x=\dfrac{3}{2}$ = 1.5 inches

Note:

[1] This question is a basic application of the unitary method.

In this method, if we are given that x items are equivalent to y objects

Then 1 item is equivalent to $\dfrac{y}{x}$ objects.

In the given question we are given that in 12 hours 18 inches of snow fell

So, we have in 1 hour $\dfrac{18}{12}=1.5$ inches of snow fell.

[2] The assumption that the distribution is uniform is necessary for the application of the unitary method. We cannot apply the unitary method if the distribution is non-uniform.

Complete step-by-step answer:

The above question can be solved by assuming that the rate of falling of snow is constant and uniform over time. This assumption is important for us to be able to solve the question.

Let us assume that the rate of falling of snow is x inches per hour.

Since the rate is uniform, the amount of snow dumped in 12 hours = 12x.

But according to the question, the amount of snow dumped in 12 hours = 18.

So, we have 12x = 18

Dividing both sides by 12, we get

$\dfrac{12x}{12}=\dfrac{18}{12}$

i.e. x = $\dfrac{3}{2}inch/hr$

Hence the amount of snow which fell in 1 hour $=x=\dfrac{3}{2}$ = 1.5 inches

Note:

[1] This question is a basic application of the unitary method.

In this method, if we are given that x items are equivalent to y objects

Then 1 item is equivalent to $\dfrac{y}{x}$ objects.

In the given question we are given that in 12 hours 18 inches of snow fell

So, we have in 1 hour $\dfrac{18}{12}=1.5$ inches of snow fell.

[2] The assumption that the distribution is uniform is necessary for the application of the unitary method. We cannot apply the unitary method if the distribution is non-uniform.

Last updated date: 18th Sep 2023

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