Respuesta :
Answer:
They are 240 kilometers apart.
Step-by-step explanation:
This question can be solved using the following relation:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
An express train travels 80km/h from Ironton to Wildwood.
Here we have [tex]v = 80, t = x[/tex]. So
[tex]v = \frac{d}{t}[/tex]
[tex]80 = \frac{d}{x}[/tex]
[tex]d = 80x[/tex]
A local train, traveling at 48km/h, takes 2 hours longer for the same trip.
This means that when [tex]v = 48, t = x + 2[tex]. So
[tex]v = \frac{d}{t}[/tex]
[tex]48 = \frac{d}{x+2}[/tex]
Since [tex]d = 80x[/tex]
[tex]48 = \frac{80x}{x+2}[/tex]
Applying cross multiplication
[tex]80x = 48(x + 2)[/tex]
[tex]80x = 48x + 96[/tex]
[tex]32x = 96[/tex]
[tex]x = \frac{96}{32}[/tex]
[tex]x = 3[/tex]
So the distance is:
[tex]d = 80x = 80*3 = 240[/tex]
They are 240 kilometers apart.
