Trains A & B are traveling if the same direction on parallel tracks. Train A is traveling at 100 miles an hour and Train B is traveling at 110 mph . Train A passes a station at 1:15 pm If Train B passes the same station at 1:45 pm what time will Train B catch up with Train A?

To find out when Train B catches up with Train A, we can begin by finding the time difference between when Train A passed the station and when Train B passed the same station.

The time difference is 1:45 pm (Train B passing time) minus 1:15 pm (Train A passing time), which is 30 minutes.

Now, we need to determine the distance Train A traveled during this 30-minute time difference. To do this, we can use the formula:

Distance = Speed × Time

Since Train A is traveling at 100 miles per hour, and the time is 30 minutes (0.5 hours), we can calculate the distance traveled by Train A:

Distance = 100 mph × 0.5 hours = 50 miles

Since Train B is catching up with Train A, the distance between them must be 50 miles at the time of Train B passing the station.

To calculate how long it will take for Train B to cover this 50-mile distance, we can use the formula:

Time = Distance ÷ Speed

Since Train B is traveling at 110 mph, the time it will take for Train B to catch up with Train A is:

Time = 50 miles ÷ 110 mph ≈ 0.4545 hours

Now, we need to convert this time from hours to minutes. We know that 1 hour is equal to 60 minutes:

Time in minutes = 0.4545 hours × 60 minutes/hour ≈ 27.27 minutes

Since we only need the time component, we can round up this value to the nearest whole number, which is 28 minutes.

Therefore, Train B will catch up with Train A approximately 28 minutes after Train B passes the station, which is at 1:45 pm. Adding these 28 minutes to 1:45 pm:

1:45 pm + 28 minutes = 2:13 pm

Thus, Train B will catch up with Train A at approximately 2:13 pm.

To find out the time when Train B catches up with Train A, we need to determine the time it takes for Train B to cover the distance that Train A has traveled. Since Train A passes the station at 1:15 pm, Train B starts chasing Train A after 30 minutes, as it passes the station at 1:45 pm.

Let's first calculate the distance traveled by Train A during this 30-minute interval:
Distance = Speed * Time
Distance = 100 mph * (30 minutes / 60 minutes)
Distance = 50 miles

Now that we know Train B needs to cover 50 miles to catch up with Train A, we can calculate the time it takes for Train B to cover this distance:
Time = Distance / Speed
Time = 50 miles / 110 mph (since Train B is traveling at 110 mph)
Time = 0.4545 hours (approximately)

To convert this time back to minutes, we multiply by 60:
Time = 0.4545 hours * 60 minutes per hour
Time ≈ 27.27 minutes

Therefore, Train B will catch up with Train A approximately 27.27 minutes after Train B starts chasing Train A. Adding this time to 1:45 pm, the time when Train B passes the station, we can determine the time Train B catches up with Train A:
1:45 pm + 27.27 minutes ≈ 2:12.27 pm

So, Train B will catch up with Train A at around 2:12.27 pm.