smc

We have a simple formula $d=rt$. The times the problem gives us, $r$ and $t$ are kind of annoying, so I will just let $x$ and $y$ be $r$ and $t$, respectively. I will also let $r_1$ and $r_2$ being the rate of the riders, where $r_1>r_2$. We can then write our equations based off these numbers, so I got $k=(r_1-r_2)x$ and $k=(r_1+r_2)y$. Rearranging the equations and solving for $r_1$ and $r_2$, I got $r_1=k/x+r_2$ (from first equation) and $r_1=k/y-r_2$ (from second equation). Also, we have $r_2=k/y-r_1$ and $r_2=-(k/x)+r_1$. Adding the first two together and the last two together, I got $2r_1=\frac{(xk+yk)}{xy}$ and $2r_2=\frac{(xk-yk)}{xy}$. Finally, dividing $2r_1$ by $2r_2$ gives us $r_1/r_2=\frac{(x+y)}{(x-y)}$. Substituting $x$ and $y$ for $r$ and $t$, I got $\boxed{\frac{r+t}{r-t}}$ -DragonFish12345 with credits to @RJ5303707 for LATEX