Chapter 6.5, Problem 24PPS

To determine

To calculate: The amount of rain in $15\min$ and $28\min$

Answer to Problem 24PPS

The required rainfall in $15\min$ is $4.29\text{inches}$ and for $28\min$ is $8\text{inches}$ .

Explanation of Solution

Given information:

The given data for rainfall record is:

  $12\text{inches}$

The given data for time record is:

  $42\text{min}$

Calculation:

Consider the ratio of rainfall and time as:

  $a:t$

Consider the given ratio of rainfall and time as:

  $12:42$

Equate the above two expression:

  $\begin{array}{l}a:t=12:42\\ \frac{a}{t}=\frac{12}{42}\end{array}$

Substitute $15\min$ for $t$ in the above equation:

  $\begin{array}{c}\frac{a}{15}=\frac{12}{42}\\ a=\frac{12}{42}\times 15\\ 42a=180\\ a=4.29\text{inches}\end{array}$

Substitute $28\min$ for $t$ in the above equation:

  $\begin{array}{c}\frac{a}{28}=\frac{12}{42}\\ a=\frac{12}{42}\times 28\\ 42a=336\\ a=8\text{inches}\end{array}$

Hence, the required rainfall in $15\min$ is $4.29\text{inches}$ and for $28\min$ is $8\text{inches}$