Problem 459

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?




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 =\frac{12}{60} = 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 =\frac{ distance}{ speed } = \frac{x}{40}

time of train B is = =\frac{ distance}{ speed } =\frac{8 +x}{60}


now put these values in our realtion







x=16 mile


now put this value in any of above relation.

like time T = \frac{distance}{speed}=\frac{x}{40}=\frac{16}{40}=0.4hour


means in minute we can say it as =0.4*60=24 minute.



train B will catch train A at 8:22+00:24=8:46PM



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