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 at 110 mph. Train A passes a station at 3:10 pm. If train B passes the same station at 3:40pm, at what time will train B catch train A?
4:30 pm
I am pretty sure that is incorrect. could someone please show me the correct expression to use to find the correct answer?
call t time after a passes
distance a = 100 t
distance b = 110 (t-.5)
-----------------------
0 = 100 t -110(t-.5)
10 t = 55
5 = 5.5 hours
3:10 + 5:30 = 8:40
When train B passes the station, train A is (1/2 h)(100 mph) = 50 miles ahead. The distance between trains decreases at 10 miles per hour. Therefore B will catch A in five hours, at 8:10 pm
Damon is correct; I should have added the 5 hours to 3:40, not 3:10
To find out the time at which train B catches up to train A, we can use the concept of relative speed. The relative speed between two objects moving in the same direction is equal to the difference in their speeds. In this case, the relative speed between train A and train B is 110 mph - 100 mph = 10 mph.
We know that train B passes the station 30 minutes (0.5 hours) after train A. To determine the time it takes for train B to catch up to train A, we need to find how long it takes for train B to cover the distance that train A has already traveled.
Distance = Relative Speed × Time
Let's denote the time it takes for train B to catch up to train A as 't'. The distance traveled by train A, which is covered by train B, can be calculated by multiplying the speed of train A by the time 't':
Distance = Speed of Train A × t
So now we have two expressions for the distance. Equating them will give us the equation we need to solve for 't':
Relative Speed × Time = Speed of Train A × t
10 mph × t = 100 mph × t
Now, we can solve this equation for 't':
10t = 100t
Subtract 100t from both sides:
10t - 100t = 0
-90t = 0
Divide by -90:
t = 0
Since the solution for 't' is 0, it means that train B catches up to train A immediately, or at the same time that train A passes the station.
Therefore, the correct answer is 3:10 pm, the same time that train A passes the station.