Chapter 12.8, Problem 2WE

To determine

To calculate: the value of, $d$ , where $r=15,\text{t}=14$ .

  $d$ varies jointly as $r$ and $t$ . If $d=45$ when $r=21$ and $t=8$ .

Answer to Problem 2WE

The value of $d$ is $36$ .

Explanation of Solution

Given information:

The value of, $d$ , where $r=15,\text{t}=14$ .

  $d$ varies jointly as $r$ and $t$ . If $d=45$ when $r=21$ and $t=8$ .

Calculation:

Consider the value of, $d$ , where $r=15,\text{t}=14$ .

  $d$ varies jointly as $r$ and $t$ . If $d=45$ when $r=21$ and $t=8$ .

Recall that the $d$ ,varies jointly as $r$ and $t$, then:

  $d=krt$

Here , If $r=15$ when $t=14$ and the value of $d=45$ .

  $\begin{array}{c}d=krt\\ 45=k\times 15\times 14\\ 45=210k\\ \frac{45}{210}=k\end{array}$

From here the value of $k$ is:

  $\begin{array}{c}\frac{45}{210}=k\\ \frac{3}{14}=k\end{array}$

Thus the equation of the variation is :

  $\begin{array}{l}d=krt\\ d=\frac{3}{14}rt\\ d=\frac{3rt}{14}\end{array}$

Now to find the value of $d$ when $r=21$ and $t=8$ .

Now apply these values in the above expression:

  $\begin{array}{c}d=\frac{3rt}{14}\\ d=\frac{3\times 21\times 8}{14}\\ d=\frac{504}{14}\\ d=36\end{array}$

Thus, the value of $d$ is $36$ .