Set 15: Systems of Equations

Choice B is correct. Choice B is the correct answer. Let $t$ = time in hours. Analysis: When traveling in opposite directions, the distances add up. - Train 1 distance: $60t$ - Train 2 distance: $80t$ - Total distance: $60t + 80 t = 140 t$ Step 1: Set up equation: $140t = 420$ Step 2: Solve for $t$: $t = \frac{420}{140} = 3$ Solution: 3 hours Verification: In 3 hours, Train 1 travels $60(3) = 180$ miles, Train 2 travels $80(3) = 240$ miles. Total: $180+ 240 = 420$ miles ✓ Strategic Tip: Opposite directions → add speeds. Same direction → subtract speeds. Choice A is incorrect because in 2 hours: $60(2) + 80(2) = 280 \neq 420$. Choice C is incorrect because in 4 hours: $60(4) + 80(4) = 560 \neq 420$. Choice D is incorrect because in 5 hours: $60(5) + 80(5) = 700 \neq 420$.