Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 mph and B is traveling at 120 mph. Train A passes a station at 9:10 pm. If train B passes the same station at 9:25pm what time will train B catch up with train A?
To solve this problem, we can calculate the time difference between when Train A passes the station and when Train B passes the same station. Since Train A passes at 9:10 pm and Train B passes at 9:25 pm, the time difference is 15 minutes.
Now, let's calculate the distance that Train A travels during this 15-minute time difference. Since Train A is traveling at a speed of 100 mph, we can calculate the distance using the formula:
Distance = Speed × Time
Distance_A = 100 mph × (15 minutes / 60 minutes per hour)
= 25 miles
This means that by the time Train B starts, Train A is already 25 miles ahead.
Now, let's determine when Train B catches up with Train A. Train B is traveling at a speed of 120 mph and needs to cover the initial distance of 25 miles to reach Train A. We can calculate the time it takes for Train B to cover this distance using the formula:
Time = Distance / Speed
Time_B = 25 miles / 120 mph
≈ 0.208 hours
Since Train B starts at 9:25 pm, we need to add the calculated time to determine when Train B catches up with Train A:
9:25 pm + 0.208 hours ≈ 9:28 pm
Therefore, Train B will catch up with Train A at around 9:28 pm.