A mathematical riddle I went through this mathematical riddle, but despite my attempts, I guess I'm missing the point. This is the riddle:
"Now, constable," said the defendant's counsel in cross-examination," you say that the prisoner was exactly twenty-seven steps ahead of you when you started to run after him?"
"Yes, sir."
"And you swear that he takes eight steps to your five?"
"That is so."
"Then I ask you, constable, as an intelligent man, to explain how you ever caught him, if that is the case?"
"Well, you see, I have got a longer stride. In fact, two of my steps are equal in length to five of the prisoner's. If you work it out, you will find that the number of steps I required would bring me exactly to the spot where I captured him."
Here the foreman of the jury asked for a few minutes to figure out the number of steps the constable must have taken. Can you also say how many steps the officer needed to catch the thief?
So I tried to make some calculations using the proportions between the real steps of the two persons, and then between the distance every step covers, but I believe something is wrong in my reasoning.
The correct answer shall be: $30$ steps, which is very different from the answer I obtain..
Any help? Thank you so much! 
 A: I think this comes down to keeping all the units straight, or rather it comes down to choosing good units to work with.
Let's fix a unit of time by saying that in each unit the prisoner travels $8$ steps and his pursuer travels $5$.  
To calculate the amount of time involved, we work in "prisoner lengths".  Since each pursuer step is $\frac 52$ of a prisoner step, in one unit of time the pursuer travels $5\times \frac 52$ lengths, and the prisoner travels $8$
Solve for the amount of time it takes to catch the prisoner.  After $n$ units of time we must have $$n\times 5\times \frac 52=n\times 8 +27\implies n=6$$
But of course the pursuer then traveled $6\times 5=30$ "pursuer steps".
A: $@user46944$ made a good point regarding whose step is considered.
Alternative approach. 
Let $m$ and $n$ be the step lengths of the constable and prisoner, respectively. Then:
$$m=\frac{5}{2}n.$$
Let $c$ and $p$ be the numbers of steps of the constable and prisoner, respectively. Then:
$$c=\frac58p.$$
Then the distance equation is (if constable's or prisoner's steps are considered, respectively):
$$D_{c}=D_{p}+27m  \ \ \ or  \ \ \ D_{c}=D_{p}+27n \Rightarrow$$ 
$$mc=np+27m  \ \ \ or  \ \ \ mc=np+27n \Rightarrow $$ 
$$\frac52nc=\frac85nc+27\cdot \frac52n  \ \ \ or  \ \ \ \frac52nc=\frac85nc+27n \Rightarrow$$ 
$$c=75 \ \ (p=120) \ \ \ or\ \ \ c=30 \ \ (p=48).$$
