Answer:
Train B will catch up to Train A at 2:45am
Step-by-step explanation:
Let's build the equations of motion for both train A and train B, starting at 1:30 AM.
These equations have the following format:
[tex]S(t) = S(0) + vt[/tex]
In which S is the position after t minutes, S(0) is the initial position and v is the velocity, in miles per hour.
Train A
Traveling at 40 mph, so [tex]v = 40[/tex].
At 1:30, 15 minutes have passed. 15 minutes is 0.25 hours. So [tex]S(0) = 0.25*40 = 10[/tex]
The equation of motion for train A is
[tex]S_{a} = 10 + 40t[/tex]
Train B
Starts at the position 0.
48 miles per hour, so [tex]v = 48[/tex]
The equation of motion for train B is
[tex]S_{b} = 48t[/tex]
If train B passes the same station at 1:30am, at what time will train B catch up to train A?
We first have to find how long it takes for train B to catch up to train A.
This is when
[tex]S_{b} = S_{a}[/tex]
[tex]48t = 10 + 40t[/tex]
[tex]8t = 10[/tex]
[tex]t = 1.25[/tex]
It is going to take 1.25 hours for the train to catch up. 1.25 hours is 60 + 0.25*60 = 75 minutes.
So train B will catch up train A 75 minutes after 1:30 am, so at 2:45am
