Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and train B at 63 mph. Train A passes a station at 11:10 AM. If train B passes the same station at 11:40 AM, at what time will train B catch up to train A?
When will train B catch up with train A?
To determine when train B will catch up with train A, we can use the concept of relative speed.
First, let's find out the time difference between when train A passes the station and when train B passes the same station.
Train A takes 30 minutes (11:40 AM - 11:10 AM) to pass the station after train A passes.
Now, we need to find out how long it will take train B to catch up to train A. To do this, we calculate the relative speed between the two trains.
The relative speed is the speed of train B minus the speed of train A, which is 63 mph - 60 mph = 3 mph.
Since train B is gaining on train A at a rate of 3 mph, the time it will take for train B to catch up to train A can be calculated using the formula:
Time = Distance / Speed.
The distance that train B needs to cover to catch up to train A is the distance between the two trains when train B passes the station.
Since train A has been traveling for 30 minutes (0.5 hours) at 60 mph, the distance covered by train A is 0.5 hours * 60 mph = 30 miles.
Therefore, train B needs to cover a distance of 30 miles in order to catch up to train A.
Using the formula, Time = Distance / Speed, we can calculate the time it will take for train B to cover 30 miles at a speed of 3 mph:
Time = 30 miles / 3 mph = 10 hours.
Therefore, train B will catch up to train A 10 hours after it passes the station.
To determine the exact time, we add 10 hours to the time train B passes the station:
11:40 AM + 10 hours = 9:40 PM.
So train B will catch up to train A at 9:40 PM.