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

`d=5t+20`

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= (\Delta d)/(\Delta t) =(10 miles)/(2hours) =5`

`\boxed{m=5}`

Now we have the full equation:

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