Answer:
Train A is travelling at a speed of 12.857 miles per hour and train B at a speed of 9.643 miles per hour.
Step-by-step explanation:
Let suppose that train A begins in position [tex]x = 0\,mi[/tex] and the train B in position [tex]x = 1.5\,mi[/tex], if [tex]v_{B} = \frac{3}{4}\cdot v_{A}[/tex] and both trains move at constant speed, then we have the following kinematic equations:
Train A
[tex]x_{A} = x_{A,o}+v_{A}\cdot t[/tex] (1)
Train B
[tex]x_{B} = x_{B,o}-v_{B}\cdot t[/tex] (2)
If both trains meet each other, then [tex]x_{A} = x_{B}[/tex]. If we know that [tex]x_{A,o} = 0\,mi[/tex], [tex]x_{B,o} = 1.5\,mi[/tex], [tex]v_{B} = \frac{3}{4}\cdot v_{A}[/tex] and [tex]t = \frac{1}{15}\,h[/tex], then we have the following expression:
[tex]x_{A,o}+v_{A}\cdot t = x_{B,o}-v_{B}\cdot t[/tex]
[tex]x_{A,o} + v_{A}\cdot t = x_{B,o} - \frac{3}{4}\cdot v_{A}\cdot t[/tex]
[tex]\frac{7}{4}\cdot v_{A}\cdot t = x_{B,o}-x_{A,o}[/tex]
[tex]v_{A} = \frac{4\cdot (x_{B,o}-x_{A,o})}{7\cdot t}[/tex]
[tex]v_{A} = 12.857\,\frac{mi}{h}[/tex]
Then, the speed of the train B is:
[tex]v_{B} = 9.643\,\frac{mi}{h}[/tex]
Train A is travelling at a speed of 12.857 miles per hour and train B at a speed of 9.643 miles per hour.
