In the figure above, car A and car B simultaneously begin traveling around a circular park with area of 4π square miles. Both cars start from the same point, the START location shown in the figure and travel with constant speed rates until they meet. Car A travels counter-clockwise and car B travels clockwise. How long will it take them to meet? (1) Car A travels twice slower than car B. (2) The sum of their speed rates is 60 mph.
A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.
(B) Knowing the area of the park, we can find its radius (πr² = 4π square miles, so r = 2 miles). Knowing the radius, we can find the length of the road (the circumference, it equals 2πr = 4π miles). To visualize this question, think about a circle as just a line segment joined at its two ends. Let’s first cut the circle at the starting point and make it into a straight line. Notice that cars A and B are at opposite ends of the line traveling toward each other. A [ ______________________ ] B
Let’s denote the speed rate of car A by x mph and the speed rate of car B by y mph. When they meet, the whole distance will be the sum of the paths they have travelled. Since they’ve started simultaneously, then they both travelled for the same time. Let’s denote it by t hours. This gives us the following relation: x × t + y × t = 4π t(x + y) = 4π t = 4π/(x + y)
Statement (1) gives us the fact that y = 2x. Still, t = 4π/(3x), which depends on x. Therefore statement (1) by itself is NOT sufficient.
Statement (2) gives us exactly the value of (x + y), so it is sufficient by itself.
Statement (2) by itself is sufficient to answer the question, while statement (1) by itself is not. The correct answer is B. ---------- This is a wrong answer.
It is, in fact possible to find out the time taken (T) by A and B to cover the respective distances from statement 1 alone. And of course as in your explanation statement 2 is sufficient. Thus the answer should be D instead of B suggested in your explaination. Please reconcile the final answer and also the explanation. Regards.
The second statement only tells you the total speed, but you do NOT know that one car is slower than the other, so speeds could be 12 and 48 or 30 and 30 or whatever.
That is correct.
Both pieces of info are required.
Knowing the sum of their speed rates is enough here, because we are asked "When will they meet?", not "Where will they meet". Knowing the sum of the speed rates we are able to tell the exact time of their meeting (counting from the start moment), even though we are not able to say where on the circle it will happen.
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