rt>0 col A: (3t+4r)/rt col B: (3t+4r)/(r+t) Which Column is greater?
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Col A
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Col B
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both are equal.
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can't be determained.
We compare (3t+4r)/rt and (3t+4r)/(r+t). Since r>0 and t>0, (3t+4r) is positive and cancels out. The comparison reduces to comparing denominators: rt vs (r+t). The relationship depends on values - if r+t > rt, Col A > Col B; if r+t < rt, Col B > Col A. Example: r=t=2 gives equality; r=3,t=2 gives Col A < Col B; r=1,t=3 gives Col A > Col B. Thus, it cannot be determined.
To determine which column is greater, let's simplify the expressions in each column.
Column A: (3t+4r)/rt Column B: (3t+4r)/(r+t)
To compare the two columns, we can cross-multiply and compare the resulting expressions.
For Column A: (rt) * (3t+4r) = 3t^2r + 4r^2
For Column B: (r+t) * (3t+4r) = 3t^2 + 7rt + 4r^2
As we can see, the expressions in Column A and Column B are not equal. Therefore, we cannot determine which column is greater without additional information.
Hence, the correct answer is D.