train A and b are traveling in the same direction on parallel tracks. Train A is traveling at 40 mph, and B is at 60 mph. Train A passes the station at 12:25 am, and train b passes the station at 12:40 am, what time will train b catch up to train A?
To determine the time at which train B catches up to train A, we need to calculate the time difference between their passages at the station.
Let's calculate this time difference:
Train A passed the station at 12:25 am, and train B passed the station at 12:40 am. The time difference between these two events is 15 minutes.
Now, we need to consider the relative speed between the two trains. Train B is traveling faster than train A, so it will gradually close the distance between them.
The relative speed between the two trains is the difference in their speeds. In this case, the relative speed is 60 mph - 40 mph = 20 mph.
Since train B needs to cover the distance that train A has already traveled, we can set up an equation to determine the time it takes for train B to catch up.
Let's denote the time it takes for train B to catch up as "t" (in hours). The equation is:
Distance covered by train B = Relative speed × Time
40t = 20t + distance covered by train A
The distance covered by train A can be calculated using its speed and the time difference between them passing the station. Since train A travels at a speed of 40 mph, the distance covered by train A in 15 minutes (0.25 hours) is 40 mph × 0.25 hours = 10 miles.
Substituting these values into the equation:
40t = 20t + 10
Simplifying the equation:
20t = 10
Solving for "t":
t = 10 / 20
t = 0.5 hours
Therefore, it will take train B 0.5 hours to catch up to train A.
To determine the time at which train B catches up to train A, we need to add this time to the time at which train B passed the station.
Train B passed the station at 12:40 am, and since 0.5 hours is equal to 30 minutes, we add the 30-minute time difference to get the final answer.
12:40 am + 30 minutes = 1:10 am
Therefore, train B will catch up to train A at 1:10 am.