John is driving around town. When he reaches the gas station, he notes that he has traveled 18 miles. He reaches home 2 hours later and notes that he has traveled 32 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
A: d=7t+18
B: d=18t+50
C: d=7t-18
D: d=14+18t
The correct equation to model this situation is A: d=7t+18.
We can determine this by looking at the given information. John traveled 18 miles when he reached the gas station, which means that at t=0 (when he reached the gas station), the distance he traveled is 18 miles. This is represented by the constant term 18 in the equation.
Furthermore, when John reaches home 2 hours later, he notes that he has traveled 32 miles. This means that when t=2 (2 hours after reaching the gas station), the distance he traveled is 32 miles. Using this information, we can substitute t=2 and d=32 into the equation and see if it holds true.
d=7t+18
32=7(2)+18
32=14+18
32=32
Since the equation holds true, we can conclude that A: d=7t+18 is the correct equation to model this situation.