Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 5:20am. If train B passes the same station at 5:35 am, at what time will train B catch up to train A?
To determine the time when train B catches up to train A, we can calculate the time difference between when train A passes the station and when train B passes the station.
We know that train A passes the station at 5:20 am, and train B passes the station at 5:35 am. Thus, the time difference between the two events is 15 minutes (35 minutes - 20 minutes).
Now, let's calculate the distance covered by each train during this time difference.
Train A, traveling at 100 miles per hour, covers a distance of:
Distance covered by train A = Speed of train A * Time = 100 miles/hour * (15 minutes / 60 minutes per hour) = 25 miles.
Now, since train B is catching up to train A from behind, it needs to cover this 25-mile distance. The relative speed of train B with respect to train A is the difference in their speeds:
Relative Speed of train B = Speed of train B - Speed of train A = 120 miles/hour - 100 miles/hour = 20 miles/hour.
To determine the time it takes for train B to cover the 25-mile distance at a relative speed of 20 miles/hour, we can use the formula:
Time = Distance / Speed = 25 miles / 20 miles/hour = 1.25 hours.
Now, to calculate the final time when train B catches up to train A, we add the time difference (15 minutes or 0.25 hours) to the time it takes for train B to cover the distance (1.25 hours):
Time = 0.25 hours + 1.25 hours = 1.5 hours.
Therefore, train B will catch up to train A 1.5 hours after train A passes the station.
To determine the final time, we add this time to the time train A passes the station:
Final Time = 5:20 am + 1.5 hours = 6:50 am.
Therefore, train B will catch up to train A at 6:50 am.