Question:
A train P takes 40 s to cross a train 800 m long and having a speed of 30 m/s in the opposite direction. It takes 120 s to cross another train twice its length and having the same speed and moving in the opposite direction to it. Find the length of the train P in metres. (a) 600 (b) 800 (c) 1000 (d) 1200
Solution:
Time taken by train P to cross 800m train= 40 s, and let length of train P= l m, speed = u m/s
Speed of 2nd train = 30m/s
Length of 2nd train = 800m
As both trains are moving in opposite direction.
Relative Speed=\({sum\, of \, lengths\, of train}\over{Time\, taken}\)
\(u + 30 = {{l + 800}\over{40}}\) ....1
Third train having same speed = u m/s
length of third train = 2×l= 2l
Relative speed of train P with respect to third.
\(u+u={{l+2l}\over{120}}\)
\(2u={{3l}\over{120}}\)
\(u={{l}\over{80}}\) ....2
Put value of u in eqn 1
\( {{l}\over{80}}+30={{l+800}\over{40}}\)
Multiplying both side by 80
\(\implies l+2400=2l+1600\)
\(\implies 2l-l=2400-1600\)
\(\implies l=800\)
So, length of train P = l = 800 m