SAT Question 70feb725: Systems of Linear Equations answer and explanation with Desmos solution

Choice D is correct. The number of hours Morgan spent running or biking can be calculated by dividing the distance she traveled during that activity by her speed, in miles per hour, for that activity. So the number of hours she ran can be represented by the expression $\frac{r}{5}$, and the number of hours she biked can be represented by the expression $\frac{b}{10}$. It's given that she biked for twice as many hours as she ran, so this can be represented by the equation $\frac{b}{10}=2\times \frac{r}{5}$, which can be rewritten as $b=4r$. It's also given that she ran $r$ miles and biked $b$ miles, and that she ran and biked a total of $200$ miles. This can be represented by the equation $r+b=200$. Substituting $4r$ for $b$ in this equation yields $r+4r=200$, or $5r=200$. Solving for $r$ yields $r=40$. Determining the number of miles she biked, $b$, can be found by substituting $40$ for $r$ in $r+b=200$, which yields $40+b=200$. Solving for $b$ yields $b=160$.