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]
