Apparently, for every k-tape Turing machine that runs in time $O(t(n))$, there exists a 1-tape Turing machine that runs in $O(t^2(n))$.
I can see how any multi-tape machine $M$ can be simulated by a 1-tape machine $S$. Just have the tape of $S$ contain all of $M$'s tapes separated by some symbol such as #.
However, why is the running time of $S$ $O(t^2(n))$ if the running time of $M$ is $O(t(n))$? I think it would be $O(t^k(n))$ since there exist $k$ tapes, and we have to traverse through all of them.