Kevin and his little brother both start at the same level. The rate that the two brothers gain levels is constant. If Kevin gains levels $1.5$ times as fast as his brother, and at the end of two hours, Kevin is six levels higher than his brother, how many levels does Kevin gain per hour?
What I did :
So I start by making equations of things I know. So since Kevin is $1.5$ times faster than his brother I can make the equation $x = 1.5y$ where $x$ is the speed of Kevin and $y$ is the speed of his brother. I plug this into the $D=rt$ equation and I get :
$$D = rt$$
$$D + 6 = 1.5y \cdot 2 $$
$$D + 6 = 3y$$
$$D = 3y - 6$$
So the equation above is for Kevin so the next equation would be for his brother
$$D = rt$$
$$D = 2y$$
So now since I can isolate $D$ on both sides I can get the equation :
$$2y = 3y - 6$$ $$y = 6$$
Since Kevin is $1.5$ times as fast as his brother $$x = 1.5y$$
$$x = 1.5(6)$$
$$x = 9$$
So would the answer be $9$? I think it is wrong because the question said he was $6$ floors higher. If anyone could help that would be great.