Respuesta :
Answer:
1)
75 kmh⁻¹
2)
75 kmh⁻¹
Explanation:
1)
[tex]v_{ab}[/tex] = Speed of train from station A to station B = 80 kmh⁻¹
[tex]d_{ab}[/tex] = distance traveled from station A to station B
[tex]t_{ab}[/tex] = time of travel between station A to station B
we know that
[tex]Time = \frac{distance}{speed}[/tex]
[tex]t_{ab} = \frac{d_{ab}}{v_{ab}} = \frac{d_{ab}}{80}[/tex]
[tex]d_{bc}[/tex] = distance traveled from station B to station C
[tex]v_{bc}[/tex] = Speed of train from station B to station C = 60 kmh⁻¹
[tex]t_{bc} = \frac{d_{bc}}{v_{bc}} = \frac{d_{bc}}{60}[/tex]
Total distance traveled is given as
[tex]d = d_{ab} + d_{bc}[/tex]
Total time of travel is given as
[tex]t = t_{ab} + t_{bc}[/tex]
Average speed is given as
[tex]v_{avg} = \frac{d}{t} \\v_{avg} = \frac{d_{ab} + d_{bc}}{t_{ab} + t_{bc}}\\v_{avg} = \frac{d_{ab} + d_{bc}}{(\frac{d_{ab}}{80} ) + (\frac{d_{bc}}{60} ) }[/tex]
Given that :
[tex]d_{ab} = 4 d_{bc}[/tex]
So
[tex]v_{avg} = \frac{4 d_{bc} + d_{bc}}{(\frac{4 d_{bc}}{80} ) + (\frac{d_{bc}}{60} ) }\\v_{avg} = \frac{4 + 1}{(\frac{4 }{80} ) + (\frac{1}{60} ) }\\v_{avg} = 75 kmh^{-1}[/tex]
2)
[tex]v_{ab}[/tex] = Speed of train from station A to station B = 80 kmh⁻¹
[tex]t_{ab}[/tex] = time of travel between station A to station B
[tex]d_{ab}[/tex] = distance traveled from station A to station B
we know that
[tex]distance = (speed) (time)[/tex]
[tex]d_{ab} = v_{ab} t_{ab}\\d_{ab} = 80 t_{ab}[/tex]
[tex]d_{bc}[/tex] = distance traveled from station B to station C
[tex]v_{bc}[/tex] = Speed of train from station B to station C = 60 kmh⁻¹
[tex]t_{bc}[/tex] = time of travel for train from station B to station C
we know that
[tex]distance = (speed) (time)[/tex]
[tex]d_{bc} = v_{bc} t_{bc}\\d_{bc} = 60 t_{bc}[/tex]
Total distance traveled is given as
[tex]d = d_{ab} + d_{bc}\\d = 80 t_{ab} + 60 t_{bc}[/tex]
Total time of travel is given as
[tex]t = t_{ab} + t_{bc}[/tex]
Average speed is given as
[tex]v_{avg} = \frac{d}{t} \\v_{avg} = \frac{d_{ab} + d_{bc}}{t_{ab} + t_{bc}}\\v_{avg} = \frac{80 t_{ab} + 60 t_{bc}}{t_{ab} + t_{bc}}[/tex]
Given that :
[tex]t_{ab} = 3 t_{bc}[/tex]
So
[tex]v_{avg} = \frac{80 t_{ab} + 60 t_{bc}}{t_{ab} + t_{bc}}\\v_{avg} = \frac{80 (3) t_{bc} + 60 t_{bc}}{(3) t_{bc} + t_{bc}}\\v_{avg} = \frac{(300) t_{bc}}{(4) t_{bc}}\\v_{avg} = 75 kmh^{-1}[/tex]
