Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 miles per hour and train B is traveling at 80 miles per hour. Train A passes a station at 5:15 A.M. IF train B passes the same station at 5:27A.M., at what time will train B catch up to train A?

At 5:27 am, train B is behind train A by

(27-15)/60*60 h*mph
= 12 mi
Train B's speed exceeds that of train A by
(80-60)=20 mph.
Can you take it from here?

A travels for time t

B travels for time (t - 12 minutes )
A goes 60 mph = 1 mile/minute
B goes 80 mph = 4/3 mile/minute
distance is the same
so
1 t = (4/3)(t-12)
3 t = 4 t - 48
t = 48 minutes
5:15 + 48 minutes = 5:63 which is 6:03

To find the time when Train B catches up to Train A, we need to determine the time difference between when Train A and Train B pass the station.

First, let's calculate the time it takes for Train A to pass the station. The time difference between 5:15 A.M. and 5:27 A.M. is 12 minutes or 12/60 hours, which is 1/5 hour.

Now let's determine the distance traveled by Train A during this time. Since Train A is traveling at a speed of 60 miles per hour, it covers 60 * 1/5 = 12 miles.

To catch up, Train B needs to cover this distance while traveling at a relative speed of 80 - 60 = 20 miles per hour (the difference in their speeds).

Given that the relative speed is 20 miles per hour, and the distance is 12 miles, we can use the formula: time = distance/speed.

The time required for Train B to catch up to Train A is 12/20 = 3/5 hours, which is equivalent to 36 minutes.

Therefore, Train B will catch up to Train A 36 minutes after it passes the station at 5:27 A.M. This corresponds to 5:27 A.M. + 36 minutes = 6:03 A.M.