Question 775842
It takes 12 seconds for two trains to pass one another when moving in opposite directions. If they are in the same direction, it will take the faster train 3 minutes to pass the slower one. If the trains are 130 meters and 120 meters long, respectively, what are the rates of the two trains?

train I speed = x
train II speed =y

When they are in opposite direction the effective speed = x+y

Time taken = 12 seconds = 12/3600  hrs. = 1/300 hours

The total length of trains is the distance d=250 m = 0.25 km

Distance = speed * time

(x+y)*1/300 =0. 250

When in same direction

effective speed = x-y
time = 3 minutes = 3/60 = 1/20 hours

(x-y)*1/20 = 0.250




(x+y)*1/300 = 0.250

x+y = 75
x-y= 5

Add the two equations

2x=80

/2
x=40 => speed of Train I

x+y=75

so speed of Train II = 75-40=35 kph