Trains a and b are traveling in the same direction on parallel tracks. Train a is traveling at 40 mph and train b is traveling at 50mph. Train a passes a station at 12:15 a.m. If train b passes the same station at 12:27a.m. at what time will train b catch up to train a??
To solve this problem, we need to determine the time it takes for Train B to catch up with Train A. We know that Train B is traveling at a higher speed compared to Train A.
Step 1: Calculate the time difference between when Train A passed the station and when Train B passed the station.
Train B passed the station 12 minutes (27 - 15 = 12) after Train A.
Step 2: Calculate the distance traveled by Train A during that time.
Using the formula: distance = speed × time
The distance traveled by Train A in 12 minutes can be calculated as:
Distance_A = speed_A × time_A
Distance_A = 40 mph × (12 minutes / 60 minutes per hour) = 8 miles
Step 3: Determine the relative speed between the two trains.
The relative speed is the difference in speed between the two trains:
Relative_speed = speed_B - speed_A
Relative_speed = 50 mph - 40 mph = 10 mph
Step 4: Calculate the time it takes for Train B to catch up with Train A.
Using the formula: time = distance / relative speed
The time it takes for Train B to catch up with Train A is:
Time = Distance_A / Relative_speed
Time = 8 miles / 10 mph = 0.8 hours
Step 5: Convert the time to minutes.
Since there are 60 minutes in an hour:
0.8 hours × 60 minutes per hour = 48 minutes
Step 6: Determine the catch-up time.
Add the catch-up time to the time when Train B passed the station:
12:27 a.m. + 48 minutes = 1:15 a.m.
Therefore, Train B will catch up with Train A at 1:15 a.m.