Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and Train B is traveling 64 mph. Train A passes a station at 7:15 AM. If Train B passes the same station at 7:45 AM, at what time will Train B catch up to Train A?
Let the time between train B passing the station and catching up to train A be t hours
so time for train A from station to catchup place is t + 1/2 hours
so I see this equation:
64t = 60(t+1/2)
which solves to t = 7.5
so the time when train B catches up to train A is 3:15 PM
(7:45 + 7:30 = 15:15 = 3:15 pm)
The previous answer is wrong. The correct answer is 1:45pm (time to catch up is 6 hours).
To find out at what time Train B will catch up to Train A, we need to determine the time difference between the two trains when Train B passes the station.
First, let's calculate the time it takes for Train A to reach the station from 7:15 AM. Since Train A is traveling at a speed of 60 mph, and it passes the station at 7:15 AM, the time it takes is given by the formula:
Distance = Speed × Time
Let the time it takes for Train A to reach the station be 't' hours. The distance covered by Train A is given by 60t miles. Since Train A passes the station at 7:15 AM, the time can be represented as t = 7:15 AM minus 7 AM.
Now, we need to determine the time difference between Train A and Train B at 7:45 AM. We know that Train B passes the same station at 7:45 AM.
The time difference is calculated as follows:
Time difference = Time taken by Train B - Time taken by Train A
Let the time difference be 'x' hours. The time taken by Train B is the same as the time taken by Train A plus 30 minutes (since 7:45 AM is 30 minutes after 7:15 AM). Therefore, the time taken by Train B is given by t + 0.5 hours.
Now we have the equation:
x = t + 0.5 - t
Simplifying the equation:
x = 0.5
So, the time difference between the two trains is 0.5 hours.
To find out at what time Train B will catch up to Train A, we add the time difference to the time Train B reaches the station. Therefore, the time will be 7:45 AM plus 0.5 hours.
Now we can find the final answer:
7:45 AM + 0.5 hours = 8:15 AM
Therefore, Train B will catch up to Train A at 8:15 AM.