Question

Hurricane Katrina dropped about 14 inches of rain over a 48 hours period. How much rain is that in inches per hour?

Answer 1

Hint:According to the question, we have to first assign a variable to the amount of rain we are going to find. Then we can keep it in a proportion format and solve for the variable by applying the rule of product of means and extremes.

Complete step by step answer:
First, we will see what is given in the question. The amount of total rain dropped was 14 inches. The total time period was over 48 hours. We need to find the amount of rain which is dropped every hour. Let us assume that the amount of rain which is dropped per hour is a variable \[x\]. Now, we can try to put the numbers in a proportion form to solve this question. When we write it in proportion form, we get:
\[14:48::x:1\]
We can also write it in another format which is:
\[ \Rightarrow 14:48 = x:1\]

Here, we will apply the product of means and product of extremes formula. The formula says that if a ratio is in a form of \[a:b = c:d\], then the product of extremes is equal to the product of means. The product of extremes is \[a \times d\]and the product of means is \[b \times c\]. So, we get:
\[a \times d = b \times c\]
Now when we apply this formula in our proportion, we get:
\[ \Rightarrow 14 \times 1 = 48 \times c\]

Now, we need to solve for \[x\]. We need to keep \[x\]alone first. We will shift 48 to the other side of the equation, and we get:
\[ \Rightarrow \dfrac{{14 \times 1}}{{48}} = x\]
This can also be written as:
\[x = \dfrac{{14 \times 1}}{{48}}\]
\[ \Rightarrow x = \dfrac{{14}}{{48}}\]
\[ \Rightarrow x = 0.291\]

Therefore, we can say that \[0.291\] inches of rain dropped per hour.

Note:Sometimes, in these questions, we have to be careful. This is because you have to convert the units from meters to inches or from hours to minutes. In this question, it was not asked but in other questions, it may ask.