Two trains, A and B, start simultaneously from opposite ends of a 450-mile track. Each travels nonstop at a uniform speed to the opposite end. A finishes its journey 4 hours after passing B, and B finishes its journey 9 hours after passing A. What were their speeds?
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Let the speeds be a and b mph, and let t be the time in hours that it takes for the two trains to meet. At that time, A and B have traveled at and bt miles, respectively. After the trains pass, A will travel the remaining bt miles in 4 hours, and B will travel at miles in 9 hours. So bt = 4a and at = 9b. This means that b = 2a/3, and as we also know that 9b + 4a = 450, a = 45 and b = 30.
From the Third Penguin Problems Book, 1946.
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