Problem 459
Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and train B is traveling at 60 miles per hour. Train A passes a station at 8:10 P.M. If train B passes the same station at 8:22 P.M. at what time will train B catch up train A?
When will train B catch up with train A?
Solution:-
Speed of train A= 40mph
and For B=60mph
Time difference between both trains is 8:22-8.10=12 minutes.
or we can say =
= 0.2hour.
now let suppose that train A will reach at (40*0.2=8 miles)distance far from the station when train B reach at station.
now suppose that Time is T when train B will catch the train A.
During this time the train A will cover distance X= 40*T
and at same time The train B will cover distance = (8+X)
now both trains have same time to reach that point. means
Time of train A= time of train B
put the values
Time of train A is =
time of train B is = =
now put these values in our realtion
3X=2(8+X)
3x=16+2x
3x-2x=16
x=16 mile
now put this value in any of above relation.
like time T = 
=0.4hour
means in minute we can say it as =0.4*60=24 minute.
now
train B will catch train A at 8:22+00:24=8:46PM