From the time the front of a train enters a platform, it takes 25 seconds for the back of thetrain to leave the platform, while travelling at a constant speed of 54 km/h. At the samespeed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as thetrain. What is the length of the train and that of the platform in meters, respectively? 210 and 140 162.5 and 187.5 245 and 130 175 and 200
Answers
1. If two objects are moving in opposite directions towards each other at speeds u and v, then relative speed = Speed of first + Speed of second = u + v.
This is also the speed at which they are moving towards each other or the speed at which they may be moving away from each other.
2. If the two objects move in the same direction with speeds u and v, then
relative speed = difference of their speeds = u – v.
This is also the speed at which the faster object is either drawing closer to the slower object or moving away from the slower object as the case may be.
Answer:
175 and 200
Explanation:
Train speed (ST) = 54 km/h = 54×(5/18) = 15m/s
Time = 25sec (for travelling length of train and length of platform)
Man speed (SM) = 9 km/h = 9×(5/18) = 2.5m/s
Relative speed = Speed of train - Speed of man
= 54 km/h - 9 km/h = 45 km/h
= 45×(5/18) = 12.5m/s
Time = 14 sec
So,
∴ Length of train = Time × Speed
= 14s × 12.5m/s
= 175m
Let Length of Platform be 'L',
Length of platform + length of train = Speed × Time
L + 175m = 15m/s × 25s
L + 175m = 375m
L = 375m - 175m
∴ Length of Platform (L) = 200m