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 5:25 A.M. If train B passes the same station at 5:37 A.M, at what time will train B catch up to train A?
To solve this problem, we need to calculate the time it takes for train B to catch up to train A.
First, let's find out the time difference between when train A passes the station and when train B passes the station:
Train A passes the station at 5:25 A.M.
Train B passes the station at 5:37 A.M.
The time difference between these two events is 12 minutes, or 12/60 = 0.2 hours.
Now, let's calculate the distance that train A has traveled during this time:
Distance = Speed × Time
Distance = 40 mph × 0.2 hours
Distance = 8 miles
Therefore, when train B starts from the station, it is already 8 miles behind train A.
Since train B is closing the gap between the two trains at a rate of 60 mph - 40 mph = 20 mph, it will take train B:
Time = Distance / Relative Speed
Time = 8 miles / 20 mph
Time = 0.4 hours = 24 minutes
Therefore, train B will catch up to train A 24 minutes after it starts from the station. To find out the exact time, we need to add this time to the time train B starts from the station:
5:37 A.M. + 24 minutes = 6:01 A.M.
So train B will catch up to train A at 6:01 A.M.