Question

assumptions:
speed of 1 st train ( =v ). speed of 2 nd train ( =u ).
combined length = total distance travelled = L When going in opposite directions with original speeds, ( v-(-u)=L / 3 )
or
( L=3 v+3 u )
now, When speed of one train is increased by ( 50 % ), and time taken is ( 2.5 mathrm{s} ) so, new speed of 1 ( v^{prime}=v+0.5 v=1.5 v )
so
( 1.5 v+u=L / 2.5 )
or
( L=3.75 v+2.5 u )
by subtracting ( 2 ) from ( 1) ( 0.75 v-0.5 u=0 )
( 1.5 mathrm{v}=mathrm{u} )
now, we have time = distance travelled / speed as the trains are moving in same direction relative velocity ( =u-v ) so, time taken ( t=L /(u-v) )
now, as ( L=3 v+3 u ) ( s 0,(a s u=1.5 v) )
( L=3 v+3^{star} 1.5 v=7.5 v )
( u-v=1.5 v-v=0.5 v )
thus,
( t=7.5 mathrm{v} / 0.5 mathrm{v}=15 mathrm{seconds} )

# U OL Uycle Two identical trains take 3 sec to pass one another when going in the opposite direction e speed of one is increased by 50 %. Find the time (in sec) one would take to pass the other when going in the same direction at their original speed. The

Solution