algebra precalculus - Why the given speed ratios are irrelevant for this problem?

The ratio of the speeds of a goods train and a passenger train is 3:7. The two trains can cross each other in 40 sec. A man in the passenger train observes that the goods train crosses him in 25 sec. If the goods train is 275m long, what is the length of the passenger train?

I proceed like this: We have to find Two trains crossing distance because two trains can crossing time is given. So Two trains crossing distance = 275 + X Other distance will be P’s distance i.e 275m

$$\begin{split} &\text{Distance ratio }= (275+X)/275\\ &\text{Time ratio }= 40/25\text{ (given)}\\ &\to (275+X)/275 = 40/25\\ &\to X = 165m \end{split}$$

Why the given speed ratios are irrelevant? why not given time ratios are irrelevant?