Question

Cameron stops to get gas soon after beginning a road trip. He checks his distance form home 2 hours after filling his gas tank and checks again 3 hours later. The first time he checked, he was 170 miles from home. The second time, he was 365 miles from home. What equation models Cameron's distance from home as a function of the time since getting gas

Answer 1

d = 40 + 65t

Explanation:

Cameron, 2 hours after filling his gas tank, checks his distance from home and 3 hours later he checks again. After the 2 hours he checked, he was 170 miles from home. Then 3 hours later, he was 365 miles from home.

Therefore, since getting gas at time(t) = 2 hours, distance from home (d) = 170 miles and at t = (2 + 3) = 5 hours, d = 365 miles.

Therefore, the equation that models the situation is

`(d - 365)/(365 - 170) = (t - 5)/(5 - 2)`

⇒ d - 365 = 65(t - 5)

⇒ d - 365 = 65t - 325

⇒ d = 40 + 65t (Answer)