Question

Snow mountain has a snow-machine that will lay down an inch of snow per hour over an area of $40,000$ square feet. Which expression shows how to find the number of hours this machine takes to lay down an inch of new snow on a ski run that is $800$ feet long and $150$ feet wide?
$\begin{align}
  & A)\dfrac{800\times 150}{40,000} \\
 & B)\dfrac{40,000}{800\times 150} \\
 & C)\dfrac{150\times 40,000}{800} \\
 & D)\dfrac{800\times 40,000}{150} \\
\end{align}$

Answer 1

Hint: In this question, we have to find an expression that finds the number of hours on the given condition. Thus, the problem is based on the area of a snow machine, thus we will use the area formula of a rectangle to get the solution. As we know, area of the rectangle is equal to the product of the length and width of the rectangular object. Thus, we will first make an expression of the area of the snow machine. Then, we know that one hour is taken to lay down the area of the snow machine, thus we will divide the equation by the area of the snow machine, to get the required solution for the problem.

Complete step by step answer:
According to the question, we have to find an expression that fulfills the given condition.
Thus, we will apply the area of the rectangle to get the solution.
Now, we know that the area of a rectangle is the product of length and width, that is
$area=length\times width$ -------- (1)
Now, we know that the length of the machine is $800$ feet long and the width is $150$ feet wide, therefore we will put these values in equation (1), we get
$area=800\times 150$
As per the statement of the problem, one hour is taken to lay down the area of snow machine that is 400 square feet, therefore
The time taken to lay down this area is equal to
$\dfrac{800\times 150}{40,000}hours$
Therefore, the expression shows the number of hours this machine takes to lay down an inch of new snow on a ski run that is $800$ feet long and $150$ feet wide is $\dfrac{800\times 150}{40,000}hours$ .

So, the correct answer is “Option A”.

Note: While solving this problem, do all the steps properly to avoid confusion and mathematical error. Do remember the area of the rectangle, which is the product of two consecutive sides. Do not forget to mention the hours with the final expression as your solution.