Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 88 miles per hour. Train A passes a station at 10:10 P.M. If train B passes the same station at 10:25 P.M. at what time will train B catch up to train A
To find out when train B will catch up to train A, we need to determine the time it takes for train B to cover the distance that train A has already traveled.
Since both trains are traveling in the same direction, the relative speed between the two trains is the difference between their speeds: 88 mph - 80 mph = 8 mph.
Now, we can calculate the time it takes for train B to catch up to train A by using the equation:
Time = Distance / Speed
Let's denote the time it takes for train B to catch up to train A as T.
The distance train A has traveled in T minutes is the speed of train A multiplied by T: 80 mph x T.
The distance that train B has traveled in T minutes is the speed of train B multiplied by T: 88 mph x T.
Since these two distances are equal when train B catches up to train A, we can set up the following equation:
80 mph x T = 88 mph x T
Simplifying the equation, we can divide both sides by T:
80 mph = 88 mph
Since this is not a valid equation, we made a mistake in our approach. Let's take a step back and reevaluate the problem.
If train B passes the station at 10:25 P.M. and train A passes the same station at 10:10 P.M., we can conclude that train B is 15 minutes behind train A.
To determine when train B catches up to train A, we need to calculate the time it takes for train B to close the 15-minute gap, considering the relative speed between the two trains, which is 88 mph - 80 mph = 8 mph.
Using the equation:
Time = Distance / Speed
We can calculate the time it takes for train B to close the 15-minute gap:
Time = (15 minutes) / (8 mph)
Converting minutes to hours:
Time = (15/60 hours) / (8 mph)
Simplifying the equation:
Time = 0.25 hours / (8 mph)
Time = 0.03125 hours
As we have the time in hours, we need to convert it back to minutes:
Time = 0.03125 hours x 60 minutes/hour
Time ≈ 1.88 minutes
Thus, train B will catch up to train A approximately 1.88 minutes after passing the station, which would be at around 10:27:52 P.M.