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John is driving around town. When he reaches the gas station, he notes that he has traveled 20 miles. He reaches home 2 hours later and notes that he has traveled 30 miles.

If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?

Respuesta :

Poltergeist

Answer:

[tex]d=5t+20[/tex]

Step-by-step explanation:

The equation that will model this situation will be of the form

[tex]d=mt+b[/tex]

where [tex]t[/tex] is the time in hours john has traveled since the gas station, and  [tex]d[/tex] is the distance.

Now we know that John has already traveled 20 miles when he is at the gas station, this means at [tex]t=0[/tex], [tex]d=20[/tex]; or

[tex]20=m(0)+b[/tex]

[tex]\boxed{b=20}[/tex]

Thus we have

[tex]d=mt+20[/tex].

Now we need to figure out [tex]m.[/tex]

When John reaches home 2 hours later he notes that he has traveled 30 miles, which means he has traveled 30 - 20 = 10 miles; thus we have

[tex]m= \frac{\Delta d}{\Delta t} =\frac{10 miles}{2hours} =5[/tex]

[tex]\boxed{m=5}[/tex]

Now we have the full equation:

[tex]\boxed{d=5t+20}[/tex]