Trains 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 5:10pm. If train B passes the same station at 5:25pm, at what time will train B catch train A.

D = RT (Distance = Rate * Time)

120 = rate of Train B
T = time of Train B
120T = distance of Train B

100 = rate of Train A
T + 0.25 = time of Train A (5:25 - 5:10 = 15 min = 60/15 = 0.25 h)
100(T + 0.25) = distance of Train A

Distances are equal
120T = 100(T + 0.25)
120T = 100T + 25
20T = 25
T = 1.25 h

Train B will catch up in 1.25 hours
I'll let you determine the time B catches train A.

Thank you. for some reason these type problems blow my mind. I cannot figure out how to put them together to solve them. I am so thankful to everyone on this site that has helped me at one time or another. THANKS!!!

You're welcome :)

train a and b are traveling in the same direction on parellel tracks. train a is traveling at 100 miles per hour and train b at 110 miles per hour.train a passes the station at8:25 and train b passes the same station at 8:55 what time will train b catch up to train a

To determine the time it takes for Train B to catch up with Train A, we need to calculate the time difference between when Train A passes the station and when Train B passes the same station.

1. Calculate the time difference between Train A and Train B passing the station:
- Train B passes the station at 5:25pm.
- Train A passes the same station at 5:10pm.
- The time difference is 5:25pm - 5:10pm = 15 minutes.

2. Convert the time difference to hours:
- 15 minutes is equal to 15/60 = 0.25 hours.

3. Determine the relative speed between Train A and Train B:
- Train A is traveling at 100 miles per hour.
- Train B is traveling at 120 miles per hour.
- The relative speed of Train B with respect to Train A is 120 - 100 = 20 miles per hour.

4. Use the formula: time = distance / speed
- The distance that Train B needs to cover to catch up with Train A is the same as the distance covered by Train A in the time difference (0.25 hours) calculated earlier.
- The speed is the relative speed between the two trains (20 miles per hour).
- Therefore, the time it takes for Train B to catch Train A is 0.25 hours / 20 miles per hour = 0.0125 hours.

5. Convert the time in hours to minutes:
- Multiply the decimal value from step 4 by 60 to convert it to minutes.
- 0.0125 hours * 60 minutes per hour = 0.75 minutes.

6. Add the time difference to the time Train B passed the station:
- 5:25pm + 0.75 minutes = 5:25pm + 0:45pm (converted from 0.75 minutes) = 6:10pm.

Therefore, Train B will catch Train A at 6:10pm.