Chapter 8.5, Problem 1GP

To determine

To find the value of $r_2$

Answer to Problem 1GP

the value of $r_2$ is $30$

Explanation of Solution

Given information:

r varies directly as t

The value of $r_1=-20$ when $t_1=4$

Calculation:

The value of $r_2$ can be obtained as

Use a proportion that relates the values

  $\frac{r_1}{t_1}=\frac{r_2}{t_2}$ [since, direct variation]

Put the values of $r_1=-20$ , $t_1=4$ and $t_2=-6$ in above equation

  $\begin{array}{l}\frac{-20}{4}=\frac{r_2}{-6}\\ (-20)(-6)=r_2(4)\left[\text{cross multiply}\right]\\ 120=4r_2\left[\text{simplify}\right]\\ r_2=30\left[\text{divide each side by 4}\right]\end{array}$

Hence,

the value of $r_2$ is $30$