Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 5:20am. If train B passes the same station at 5:35 am, at what time will train B catch up to train A?
A travels time t
B travels time (t-.25hr)
distance = d = rate * time
100 t = 120(t-.25)
you can solve that
To determine the time when train B will catch up to train A, we need to calculate the time difference between when train A passed the station and when train B passed the station. We can use the relative speed of train B with respect to train A to calculate this.
From the given information, we know that train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. This means that train B is gaining on train A at a relative speed of 120 - 100 = 20 miles per hour.
Since train A passed the station at 5:20 am and train B passed the same station at 5:35 am, the time difference between their passages is 15 minutes or 1/4 hour.
Now, we can use the formula: time = distance / speed to find the time it takes for train B to catch up to train A.
Let's assume the distance covered by train B from the station to the catch-up point is D miles.
For train A, the time taken to cover this distance D is given by: time = D / 100.
For train B, the time taken to cover the same distance D is given by: time = D / 120.
Since train B takes 1/4 hour longer to cover the same distance D, we can set up the equation: D / 120 = D / 100 + 1/4.
To solve for D, we can cross-multiply and then simplify the equation:
4D = 3D + 30
4D - 3D = 30
D = 30
Thus, the distance covered by both trains from the station to the catch-up point is 30 miles.
Finally, to find the time when train B catches up to train A, we can substitute the distance D into either of the time equations. Let's use the equation for train B:
time = D / 120
time = 30 / 120
time = 1/4 hour
Therefore, train B will catch up to train A 1/4 hour after train A passed the station.
To find the exact time, we add 1/4 hour (15 minutes) to the time train A passed the station, which was 5:20 am.
Thus, train B will catch up to train A at 5:20 am + 15 minutes = 5:35 am.
Therefore, train B will catch up to train A at 5:35 am.