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A driver travels from town A to town B at a constant speed, and then from town B to town C at a different constant speed. He takes 4 hours to go from A to B, and the same time to go from B to C, even though the distance from B to C is 30 km greater. If his overall average speed is 80 km/h, find the distances between the three towns

Respuesta :

Answer:

distance between A and B = 305 km

distance between B and C = 335 km

Step-by-step explanation:

Linear Motion with Constant Velocity:

[tex]\boxed{distance\ (s)=velocity\ (v)\times time\ (t)}[/tex]

[tex]\boxed{average\ velocity\ (\overline{v})=\frac{total\ distance\ (\Sigma s)}{total\ time\ (\Sigma t)} }[/tex]

Given:

[tex]t_{AB}=t_{BC}=4\ hours[/tex]

[tex]s_{AB}+30=s_{BC}[/tex]

[tex]\overline{v}=80\ km/h[/tex]

[tex]\Sigma t=t_{AB}+t_{BC}[/tex]

    [tex]=4+4[/tex]

    [tex]=8\ hours[/tex]

[tex]\Sigma s=s_{AB}+s_{BC}[/tex]

    [tex]=s_{AB}+s_{AB}+30[/tex]

    [tex]=(2s_{AB}+30)\ km[/tex]

[tex]\displaystyle \overline{v}=\frac{\Sigma s}{\Sigma t}[/tex]

[tex]\displaystyle 80=\frac{2s_{AB}+30}{8}[/tex]

[tex]2s_{AB}+30=80\times8[/tex]

[tex]2s_{AB}=640-30[/tex]

[tex]s_{AB}=610\div2[/tex]

[tex]\bf s_{AB}=305\ km[/tex]

[tex]s_{AB}+30=s_{BC}[/tex]

[tex]305+30=s_{BC}[/tex]

[tex]\bf s_{BC}=335\ km[/tex]

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