SOLUTION: Hello! Can someone help please? My question is: Two trains travel in the same direction at 50 kilometres per hour and 32 kilometres per hour respectively. A man in the slowe

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Question 43373: Hello!
Can someone help please?
My question is:
Two trains travel in the same direction at 50 kilometres per hour and 32 kilometres per hour respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes him.
What is the length of faster train?
Thank you for your help and time.
geomar
Found 2 solutions by longjonsilver, psbhowmick:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
from the viewpoint of the man on the slower train, he is stationary and the faster train is going at 18kmph. This is the basics of "relativity".

Anyway, we now have speed and time. We can therefore find the length.

First we need all numbers to have consistent units. We have speed in kmph and a time in seconds. We need to convert kmph into km per second OR convert the 15 seconds into hours. The second is easier

Start with something you know:
60 seconds = 1 minute
so 1 second = 1/60 minutes
and hence 15 seconds = 15/60 minutes

so, 15 seconds = 1/4 minute

Again, start with something we know:
60 minutes = 1 hour
so 1 minute = 1/60 hours
and hence 1/4 minutes = (1/4)*(1/60) hours

so 15 seconds = 1/240 hours

speed = distance/time
so distance = speed*time
--> distance = 18*(1/240)
distance = 0.075km

and converting this to something more meaningful, we have distance = 75m

So, length of train is 75m long.

Jon.

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
As both the trains are moving in same direction, so the relative speed of the faster train with respect to the slower train = (50 - 32) = 18 km/hr.
As the man is sitting inside the slower train so, to him, the slower train is at rest and the faster train is moving at a speed of 18 km/hr.
The faster train passes the man in 15 seconds.
This means that the faster train travels a distance equal to its own length in 15 seconds, relative to the man inside the slower train.

Use this formula: red%28DISTANCE+=+SPEED+x+TIME%29.
To use this formula we have to use similar units for speed and time.
Here speed is in km/hr. We have to convert it to m/s.
1+km%2Fhr+=+%281000+m%29%2F%283600+s%29+=+5%2F18 m/s
So 18 km/hr = 5%2A18%2F18 = 5 m/s
The distance traveled by the faster train in 15 seconds at a relative speed of 18 km/hr, as given by the formula, is 5 x 15 = 75 m

Hence, the length of the faster train is 75 m.