1) What is the speed of the train whose length is 210 metres?
I. The train crosses another train (Howrah Express/12869) of 300 metres length running in opposite direction in 10 seconds.
II. The train crosses another train (Howrah Express/12869) running in the same direction at the speed of 60 km/hr in 30 seconds.
Explanation:
Time taken to cross the train, running in opposite directions = [(l1 + l2)/ (u + v)] sec.
=> 10 = [ (210 + 300)/ (u + v) ]
=>u + v = 51.
Time taken to cross the train, running in same direction = [ (l1 + l2)/(u - v)] sec.
=> 30 =[ (210 + 300)/ (u - 60 x (5/18)) ]
=> u = [ ( 17 +(50/3) ] m/sec.
Thus, u and v can be obtained.
2) What is the length of a running train crossing another 180 metre long train running in the
opposite direction?
I. The relative speed of the two trains was 150 kmph.
II. The trains took 9 seconds to cross each other.
Explanation:
Let the two trains of length a metres and b metres be moving in opposite directions at u m/s
and v m/s.
Time taken to cross each other = [ (a + b)/ (u + v) ] sec.
Now, b = 180, u + v = [ 150 x (5/18) ] m/sec = (125/3 ) m/sec.
=> 9 = [ (a + 180)/ (125/3) ]
=> a = (375 - 180) = 195 m.
3) What is the length of a running train?
I. The train crosses a man in 9 seconds.
II. The train crosses a 240 metre long platform in 24 seconds.
Explanation:
Time taken by train to cross a min = ( Length of train/ Speed of train )=> Speed
= (l/9)....(i)
Time taken by train to cross a platform =[ (Length of train +Length of platform)/ Speed of
train ] =>Speed = (l + 240)/24 ....(ii)
From (i) and (ii), we get l/9 = [ (l + 240)/24 ].