I don't understand can someone help me on how to figure this out please !!
Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hour an train B is traveling at 100 miles per hour. Train A passes a station at 2:25 pm. If train B passes the same station at 2:37 pm,. at what time will train B catch up to train A?
why did train b which is traveling faster then train a, need to catch up to train a? doesn't make sense.did train b stop somewhere along the way, or did train be have a different starting point?
That's the question asked on the homework.
not enough facts present or the there's a misprint.
a formula useful for similar equations, though, is distance = rate x time
Let the station be at x = 0. After 2:37 pm, train A is at
x(A) = (2:37-2:25)/(60 minutes per hour)*80 mph + 80 * t,
or
x(A) = (12 min / 60 min per hour) * 80 mph + 80 * t
x(A) = 16 + 80 * t
where t is hours after 2:37
for train B,
x(B) = 100*t
Set x(A) = x(B) or
100*t = 16 + 80*t
20*t = 16
t = 3/4 hour
Add this time to 2:37 to find the time when they catch up with each other
To determine the time when train B catches up to train A, we need to calculate the time difference between when train A passes the station and when train B passes the same station.
First, let's find the time difference between train A passing the station and train B passing the same station:
Train A passes the station at 2:25 pm.
Train B passes the station at 2:37 pm.
To find the time difference, we subtract the earlier time from the later time:
2:37 pm - 2:25 pm = 12 minutes.
So, the time difference between train A passing the station and train B passing the same station is 12 minutes.
Now, since train B is traveling at a higher speed than train A, it will gradually catch up to train A. To calculate the catching up time, we need to determine how much distance train B covers in the 12 minutes time difference.
Given that train A is traveling at a speed of 80 miles per hour and train B is traveling at a speed of 100 miles per hour, we know that train B is gaining on train A at a relative speed of 100 mph - 80 mph = 20 mph.
To find the distance train B covers in 12 minutes, we convert the 12 minutes into hours:
12 minutes / 60 minutes per hour = 0.2 hour
Now, we can calculate the distance train B covers in 0.2 hour:
Distance = Speed × Time
Distance = 20 mph × 0.2 hour
Distance = 4 miles
Therefore, train B covers 4 miles in the 12 minutes (time difference) and will catch up to train A when the distance between them is 4 miles.
Finally, we need to determine how long it will take for train B to cover the remaining distance after the initial 12-minute catching up time at a speed of 20 mph relative to train A.
To calculate this, we divide the remaining distance (4 miles) by the relative speed (20 mph):
Time = Distance / Speed
Time = 4 miles / 20 mph
Time = 0.2 hour
Convert 0.2 hours to minutes:
0.2 hour × 60 minutes per hour = 12 minutes
Therefore, train B will take an additional 12 minutes to catch up to train A after the initial time difference of 12 minutes.
To find the total catching up time, we add the initial time difference (12 minutes) and the additional time (12 minutes):
12 minutes (initial time difference) + 12 minutes (additional time) = 24 minutes
Therefore, train B will catch up to train A after 24 minutes, or at 2:37 pm + 24 minutes = 3:01 pm.
In summary, train B will catch up to train A at 3:01 pm.