Trains A and B are traveling the same direction on parallel tracks. Train A is traveling at 100 mph and train B is traveling 110 mph. Train A passes a station at 6:10 A.M. If train B passes the same station at 6:40 A.M. at what time will train B catch up with Train A?
They are 1/2 hour apart. To catch up, they have to travel the same distance.
d=100(t)
d=110(t-.5)
set them equal
100t=110t-55
55=10t
t= 5.5 hrs.
check my thinking.
would that be 11:30 am?
To determine the time when train B catches up with train A, we need to calculate the time it takes for train B to cover the distance between the station and catch up with train A.
First, we need to find the head start that train A has. Train A passes the station at 6:10 A.M. and train B passes the same station at 6:40 A.M. This means that train A has a head start of 30 minutes, or 0.5 hours.
Next, we need to calculate the distance train A travels during this 30-minute head start. Since train A is traveling at a constant speed of 100 mph, the distance it covers in 0.5 hours is:
Distance = Speed * Time = 100 mph * 0.5 hours = 50 miles.
Now, we can consider the relative speed between the two trains. Train B is traveling at a speed of 110 mph, which is 10 mph faster than train A. This is the relative speed at which train B is gaining on train A.
To determine the time it takes for train B to catch up with train A, we divide the distance train A has already traveled (50 miles) by the relative speed of train B:
Time = Distance / Relative Speed = 50 miles / 10 mph = 5 hours.
Now, we add this time to the time train B passes the station (6:40 A.M.) to find the time when train B will catch up with train A:
6:40 A.M. + 5 hours = 11:40 A.M.
Therefore, train B will catch up with train A at 11:40 A.M.