(a) 30 kmph Let, the speed of the trains be S1 and S2 respectively. Length of each train = 100 m When trains are going in the same direction, then Relative speed =
Sumoflengthoftrains
Timetakentocrosseachother
⇒ S1−S2 =
100+100
60
=
200
60
m/sec ⇒ S1−S2 =
10
3
m/sec =
10
3
×
18
5
= 12 km/hr .......(i) When trains are going in opposite direction, then S1+S2 =
100+100
10
=
200
10
⇒ S1+S2 = 20 m/sec = 20 ×
5
18
km/hr ⇒ S1+S2 = 72 km/hr ......(ii) From Eqs. (i) and (ii), S1 = 42 kmph, S2 = 30 kmph ∴ Speed of slower train is 30 kmph.