How do we determine how much time a multi-tape DTM saves over a one-tape DTM?
As this is homework, I'll go for the gentle hint approach. Firstly, it's a bit odd to talk about a TM using an algorithm - a TM is an algorithm, so my interpretation of the question is:

Given a multitape TM, you want to produce a single tape TM that does the same job (i.e. has the same language), and you want to know how much slower the single tape version is (in the worst case).

To put it another, hint laden way, how much slower is it to simulate a multitape machine with a single tape machine?

There's a rather important result regarding this (i.e. there's a way to do it that guarantees an upper bound on the slowdown factor), a little searching should get you that at least.