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Pablo drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Pablo drove home, there was no traffic and the trip only took 4 hours. If his average rate was 40 miles per hour faster on the trip home, how far away does Pablo live from the mountains?

Respuesta :

Using the relation between velocity, distance and time, it is found that Pablo lives 288 miles away from the mountains.

What is the relation between velocity, distance and time?

  • Velocity is distance divided by time, that is:

[tex]v = \frac{d}{t}[/tex]

Going to the mountain:

  • Velocity v.
  • Distance d.
  • Time of 9 hours, hence [tex]t = 9[/tex].

Then, considering we want the distance:

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{d}{9}[/tex]

[tex]d = 9v[/tex]

[tex]v = \frac{d}{9}[/tex]

Returning from the mountain:

  • 40 miles per hour faster on the trip home hence the velocity is v + 40.
  • Distance d.
  • Time of 4 hours, hence [tex]t = 4[/tex].

Then:

[tex]v + 40 = \frac{d}{4}[/tex]

[tex]d = 4v + 160[/tex]

Since [tex]v = \frac{d}{9}[/tex]:

[tex]d = \frac{4d}{9} + 160[/tex]

[tex]d - \frac{4d}{9} = 160[/tex]

[tex]\frac{5d}{9} = 160[/tex]

[tex]d = \frac{160(9)}{5}[/tex]

[tex]d = 288[/tex]

Pablo lives 288 miles away from the mountains.

You can learn more about the relation between velocity, distance and time at https://brainly.com/question/24316569

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