Question

John is driving around town. When he reaches the gas station, he notes that he has traveled 10 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?
A. d = 10t - 10

B. d=20 + 10 t

C. d= 10t + 10

D. d= 10t + 40

Answer 1

C. d= 10t + 10
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Answer 2

C. d = 10t + 10

Explanation:

If d represents the distance, you know that the equation on the other side has to have +10 included in it because this was stated in the problem (he has traveled 10 miles). C is the only option with +10, but if you'd like a further explanation on the 10t part... by the end of his trip, he has traveled 30 miles total. Subtract the 10 he initially traveled before arriving at the gas station, and he has traveled 20 miles in two hours. 20 (miles) / 2 (hours) = 10, so after the gas station, he traveled at an average speed of 10 mph. We now know that he traveled 10 miles, plus another 10 miles for every additional hour (t) he travels after that. This gives us d = 10t + 10.