Having trouble understanding the relationship between these expressions

[coldjeanz]

I understand everything up until:

√MgL/m = L/t

Why is that equal to L/t?

I also don't understand this either:

This is the problem itself however I don't feel it's that important since I am trying to figure out how they are arriving at their conclusions.

An astronaut on a small planet wishes to measure the local value of the free-fall acceleration by timing pulses traveling down a wire that has an object of large mass suspended from it. Assume a wire has a mass of 4.10 g and a length of 1.60 m and that a 3.00 kg object is suspended from it. A pulse requires 43.6 ms to traverse the length of the wire. Calculate g of planet from these data. (You may ignore the mass of the wire when calculating the tension in it.)

 

[Steely Dan]

They are not saying that the last equality follows from something about $\sqrt{MgL/m}$, but rather that the wave speed $v$ is equal to both $\sqrt{T/u}$ AND $L / t$ (since speed is just distance divided by time).

The second section is just an algebraic rearrangement of the second equation in the first section.

 

[coldjeanz]

Yeah okay that went through my head for a split second but I couldn't find that in my book so I didn't know where they pulled it from. Thank you!