# 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?

• because all you care about is the combined speed of two trains Commented Nov 4, 2019 at 16:50
• @Vasya what combined speed are you referring to? I am asking why given speed ratios are irrelevant? why not given time ratios are irrelevant? Commented Nov 4, 2019 at 17:05
• Because trains are moving in opposite directions, the speed of crossing is equal to sum of two speeds. Thus the ratio of them is irrelevant. Commented Nov 4, 2019 at 17:07
• @Vasya what if trains are moving in same directions, then time ratio will be irrelevant? Commented Nov 4, 2019 at 17:11
• The ratio is needed if you need to find the speed of each train. Think about it: if two objects which are 100 meters apart and they meet after 10 seconds, the combined speed/rate is 10 m/s. Individual speeds do not matter, as long as the sum of them is 10 m/s. Commented Nov 4, 2019 at 17:16