Trains A and B trave in same direction parallel tracks. A is traveling100 miles /hr. B is traveling 120 miles/hr. A passes a station at 1:10 and B at 1:25 When will B catch up to A?

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B will catch up to A when they have both gone the same distance past the station.  So, if we get expressions for both of their Distances, we can set those equal to each other for our equation.  B's rate was 120 and we do not know it's time, so we call that x.  Since D = RT, that makes D for this train 120x.A's rate was 100 and we do not know it's time, but we do know that it had a .25 hour (15 minutes is .25 hours) head start on B.  Since we called B's time x, we can then call A's time (x + .25).  D = RT, so A's D is going to be 100(x + .25).  Now we set both of these expressions for our D's equal to each other for our equation.120x = 100(x + .25)Distribute the 100.120x = 100x + 25Subtract 100x from both sides.20x = 25Divide both sides by 20.x = 1.25So, B will catch up to A after 1.25 hours.  What time will that be?  Well, 1.25 hours is 1 hour and 15 minutes.  Add that to the starting time of 1:25 and we get that B catches up at 2:40.