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?

When train B passes, train A is ahead by 40 miles/hr x (0.2 hr) = 8 miles.

Therafter, the distance between the trains decreases at a rate (60 - 40) = 20 mph. The gap disappears after 8/20 h = 24 minutes.

24 minutes after 5:37 is 6:01 AM

You can also do this with equations, but my way is quicker.

A travels 12 minutes or 12/60 = 1/5 hour longer that B

If A travels t hours, B travels (t-1/5) hours
They go the same distance (rate*time)
so
40 t = 60(t-1/5)
get t
change it to minutes by multiplying by 60
add it to when A passed the station.

To find the time when train B catches up to train A, we need to determine the time difference between when train A passes the station and when train B passes the same station.

The time difference between when train A and train B pass the station is 12 minutes (37 - 25 = 12).

Now, we need to calculate how much distance train A covers in this 12-minute time difference.

Since train A is traveling at 40 miles per hour, we can convert this to miles per minute by dividing it by 60 (40 / 60 = 2/3 miles per minute).

Distance covered by train A in 12 minutes = (2/3 miles per minute) x 12 minutes = 8 miles.

Since train B needs to cover this 8-mile distance to catch up to train A, we can now calculate how long it will take for train B to cover the distance.

Since train B is traveling at 60 miles per hour, we can convert this to miles per minute by dividing it by 60 (60 / 60 = 1 mile per minute).

Time taken for train B to cover 8 miles = 8 miles / 1 mile per minute = 8 minutes.

Therefore, train B will catch up to train A 8 minutes after train A passes the station.

To find the time when train B catches up to train A, we add the 8-minute catching up time to the time train A passes the station, which is 5:25 A.M.

5:25 A.M. + 8 minutes = 5:33 A.M.

Thus, train B will catch up to train A at 5:33 A.M.