Question

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?

Answer 1

Answer:

$d=5t+20$

Step-by-step explanation:

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

$d=mt+b$

where $t$ is the time in hours john has traveled since the gas station, and  $d$ is the distance.

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

$20=m(0)+b$

$\boxed{b=20}$

Thus we have

$d=mt+20$.

Now we need to figure out $m.$

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

$m= \frac{\Delta d}{\Delta t} =\frac{10 miles}{2hours} =5$

$\boxed{m=5}$

Now we have the full equation:

$\boxed{d=5t+20}$