# Regarding time complexity of multi-tape Turing machines

So let's say I've implemented an algorithm running in $$O(n^2)$$ on my 3-tape TM. What kind of time complexity would I expect for a single-tape TM?

I just don't know where to get started...

Multi-tape Turing Machine running in $$O(f(n))$$ can be simulated by a single-tape Turing machine running in $$O(f^2(n))$$.
Try writing a single-tape Turing machine that stores symbols from your $$3$$ tapes on its one tape, separated by some unique symbol not in $$\Sigma$$.
hint: For every step of your $$k$$-tape machine, a one-tape machine must first do at most $$k\cdot n$$ steps to find the position.