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