Trains A and B are traveling in the same direction on parallel tracks. Train a is traveling at 100 mph and train B is traveling 120 mph. Train a passes a station at 7:20 P.M. If train B passes the same station at 7:35 P., at what time will train B catch up to train A?
By 7:35, train A would have gone 15min. past the station. The distance travelled would have been 100 mph*15/60 hours = 25 miles.
Train B catches up at the rate of 120-100 mph=20 mph. How long would it take to catch up?
7:35 PM - 7:20 PM = 15 min = 0.25 h,
When train B catches up with A, their
distance traveled will be equal. But A
traveled that distance in 15 min(0.25h)
less. Therefore:
d1 = d2,
100t = 120(t - 0.25),
100t = 120t - 30,
100t - 120t = -30,
-20t = -30,
t = 1.5 h = train A time traveled.
(t - 0.25) = 1.5 - 0.25 = 1.25 h =
1:15 = Time needed for B to catchup,
B caughtup at: 7:35 PM + 1:15 = 8:50PM.
To find the time when train B catches up to train A, we need to calculate the time difference between when they passed the station.
First, we need to determine the time difference between when train A passed the station and when train B passed the station.
Train A passed the station at 7:20 P.M., and train B passed the same station at 7:35 P.M. Therefore, the time difference is 15 minutes (7:35 - 7:20 = 15 minutes).
Now, let's find the distance that train A traveled during this time.
Since both trains are traveling in the same direction, the distance train A travels during this time is the speed of train A multiplied by the time difference.
Speed = 100 mph
Time difference = 15 minutes = 15/60 hours = 1/4 hours (since 1 hour = 60 minutes)
Distance traveled by train A = Speed of train A * Time difference
Distance traveled by train A = 100 mph * 1/4 hours = 25 miles
Now, we know that when train B catches up to train A, they will have traveled the same distance. So, we need to find the time it takes for train B to travel this distance.
The relative speed of train B with respect to train A is the difference in their speeds.
Relative speed = Speed of train B - Speed of train A
Relative speed = 120 mph - 100 mph = 20 mph
To find the time it takes for train B to catch up, we divide the distance traveled by the relative speed.
Time = Distance traveled by train A / Relative speed
Time = 25 miles / 20 mph = 1.25 hours
Now, let's calculate the time at which train B catches up to train A.
Train B passed the station at 7:35 P.M., and it takes 1.25 hours for train B to catch up to train A.
Therefore, the time when train B catches up to train A is 7:35 P.M. + 1 hour 15 minutes = 8:50 P.M.
So, train B will catch up to train A at 8:50 P.M.