I am so lost can someone please help me
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 100 miles per hour. Train A passes a station at 11:15am. If train B passes the same station at 11:27a.m., at what time will train B catch up with train A?
At 11:27, when B is at the station, train A will have traveled 12 minutes at 80 mph for a distance of 80(1/60) or 16 miles
So draw a line with B at the station on the left, A 16 miles to the right of B.
Let the distance that A still travels before B catches up be x miles, call that point P
So AP = x, BP = x+16
Time for B to reach P is (x+16)/100
time for A to reach P is x/80
but those times are equal, so
(x+16)/100 = x/80
.
.
x = 64
so time for A to reach P is 64/80 = .8 hrs, or 48 minutes.
so the time when it happens is 11:27 + 0:48 = 1:15 pm
To find out at what time train B will catch up with train A, we can use the concept of relative motion.
First, we need to determine the time difference between when train A and train B passed the station. Train A passed the station at 11:15am, and train B passed the same station at 11:27am. Therefore, the time difference is 11:27 - 11:15 = 12 minutes.
Next, we need to find out how far train A travels in the time difference of 12 minutes. Since train A is traveling at a constant speed of 80 miles per hour, we can calculate the distance traveled by using the formula:
Distance = Speed x Time
Distance = 80 miles/hour x (12 minutes / 60 minutes)
Distance = 80 miles/hour x (0.2 hours)
Distance = 16 miles
Now that we know the distance that train A has traveled, we need to determine how long it will take train B to cover the same distance. Since train B is traveling at a speed of 100 miles per hour, we can use the formula:
Time = Distance / Speed
Time = 16 miles / 100 miles/hour
Time = 0.16 hours
Finally, we add the time difference of 12 minutes to the time it takes for train B to cover the same distance as train A:
Total Time = 0.16 hours + (12 minutes / 60 minutes)
Total Time = 0.16 hours + 0.2 hours
Total Time = 0.36 hours
To determine the catch-up time, we add the total time to the time train B passed the station:
Catch-up Time = 11:27am + 0.36 hours
Catch-up Time = 11:27am + 0 hours 36 minutes
Catch-up Time = 11:27am + 36 minutes
Catch-up Time = 12:03pm
Therefore, train B will catch up with train A at 12:03pm.