Bunuel wrote:
Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist A travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?
A. 275
B. 250
C. 225
D. 215
E. 210
The two speeds have a direct proportion, the ratio of A's speed to B's is \(1 : \frac{2}{3}\) or \(3:2\). Since they both travel the same amount of time, their distance covered must also have a ratio of \(3:2\). We also know the total distance is 375 miles. Then they will split the 375 miles into 5 equivalent portions, 3 portions belong to A and 2 other portions belong to B. Hence 3/5's of the total distance is traveled by A and the rest by B. \(375 * \frac{3}{5} = 225\).
Ans: C
Once the student masters this ratio method, the only calculation required is 3+2 = 5 then \(375 * \frac{3}{5} = 225\).
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