Set 9: Systems of Equations (Intermediate)

Choice B is correct. Choice B is the correct answer. When traveling in the same direction, the faster car pulls ahead. Let $t$ = time in hours. Analysis: The difference in distances equals 45 miles: $$$70t - 55 t = 4515t = 45$t = 3 Solution: 3 hours Verification: After 3 hours: - Car A: $55(3) = 165$ miles - Car B: $70(3) = 210$ miles - Difference: $210- 165 = 45$ miles ✓ Strategic Tip: Same direction → subtract speeds to find rate of separation. Choice A is incorrect because $70(2) - 55(2) = 140 - 110 = 30 \neq 45$. Choice C is incorrect because $70(4) - 55(4) = 280 - 220 = 60 \neq 45$. Choice D is incorrect because $70(5) - 55(5) = 350 - 275 = 75 \neq 45$.