Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 mph and train B is traveling at 110 mph. Train A pases a station at 4:10 a.m. If train B passes the same station at 4:22 a.m., at what time will train B catch up to train A?
4:22 - 4:10 = :12 min = 0.2 h = make-up time for train B.
Train A time = t hrs,
Train B time = (t - 0.2) hrs.
d(A) = d(B) = Distance traveled.
100t = 110(t - 0.2),
100t = 110t - 22,
100t - 110t = -22,
-10t = -22,
t = 2.2 hrs,
(t - 0.2) = 2.2 - 0.2 = 2.0 hrs =
time to catchup.
To find out when train B will catch up to train A, we need to determine the time difference between when train A passes the station and when train B passes the same station.
First, we need to calculate the time difference between the two trains passing the station.
Train A passes the station at 4:10 a.m., and train B passes the station at 4:22 a.m., so the time difference is 12 minutes or 12/60 hours.
Next, we need to calculate the distance that train B needs to cover to catch up to train A.
Since train B is traveling faster than train A, it is gradually closing the gap between them. The relative speed between the two trains is the difference between their speeds, which is 110 mph - 100 mph = 10 mph.
Now, let's use the formula Distance = Speed * Time to find the distance train B travels in the time it takes to catch up to train A.
Let's represent the time it takes for train B to catch up to train A as T hours.
The distance traveled by train B in T hours is 10 mph * T.
At the current time difference of 12/60 hours, train A has traveled a distance of 100 mph * (12/60) = 20 miles.
Since train B needs to catch up to train A, the distance it travels (10 mph * T) should be equal to the distance train A has already traveled (20 miles).
Therefore, the equation is 10 mph * T = 20 miles.
Solving for T, we have T = 20 miles / 10 mph = 2 hours.
So, it will take train B 2 hours to catch up to train A.
Adding the 12 minutes or 12/60 hours of the time difference to the time when train B passes the station (4:22 a.m.), we can determine when train B will catch up to train A.
4:22 a.m. + 12 minutes = 4:34 a.m.
Therefore, train B will catch up to train A at 4:34 a.m.