Respuesta :
Answer:
The usual duration of the train journey from station A to B is [tex]6[/tex] hours.
Step-by-step explanation:
Lets try to understand with a real life example of the question then we will frame it in terms of variables.
As given the train starts from [tex]7[/tex] am and reached the destination at [tex]1[/tex]pm.
When it is late by two hours it started its journey at [tex]9[/tex]am so will reach at [tex]3[/tex] pm as it has already covered up with an hour due to increased in its speed then actually it reached at [tex]2[/tex] pm.One hour late from its scheduled time.
Lets frame an equation.
Knowing the fact distances are same for both of the station.
And [tex]Distance = Speed\times time[/tex]
Now we take [tex]s[/tex] as our normal day speed and [tex]s+0.2s=1.2s[/tex] speed when the train is late, [tex]\frac{20}{100}=0.2[/tex] is added with the previous speed.
Similarly with time [tex]t[/tex] as our normal time and [tex](t-1)[/tex] when the train is running late from its scheduled time.
Now
[tex]d_{1}=s\times t[/tex] on normal days.
[tex]d_{2}=1.2s(t-1)= 1.2st-1.2s[/tex] when the train is late.
Equating both the equations as distances are same.
We have
[tex] st = 1.2st-1.2s[/tex]
Subtracting [tex]st[/tex] from both sides.
[tex]0.2st-1.2s=0[/tex]
Taking [tex]s[/tex] as common terms.
The remaining equation is
[tex]0.2t-1.2=0[/tex]
Adding [tex]1.2[/tex] both sides
[tex]0.2t=1.2[/tex]
[tex]t=\frac{1.2}{0.2} =6[/tex]
So the journey fro station A to b is of [tex]6[/tex] hours.
