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The figure shows Tap A, Tap B and an empty tank. Tap A can fill the empty tank in 12 minutes and Tap B can fill the empty tank in 6 minutes. Both taps are turned on at the same time. How long will it take for both taps to fill up the whole tank together?

Question

The figure shows Tap A, Tap B and an empty tank. Tap A can fill the empty tank in 12 minutes and Tap B can fill the empty tank in 6 minutes. Both taps are turned on at the same time. How long will it take for both taps to fill up the whole tank together?

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Solution

To solve this problem, we need to find the combined rate of the two taps.

  1. First, we find the rate of each tap. The rate of Tap A is 1 tank per 12 minutes, or 1/12 tanks per minute. The rate of Tap B is 1 tank per 6 minutes, or 1/6 tanks per minute.

  2. Next, we add these rates together to find the combined rate. The combined rate of Tap A and Tap B is 1/12 + 1/6 = 1/4 tanks per minute.

  3. Finally, we find the time it takes for both taps to fill the tank together. Since rate is the reciprocal of time, the time it takes is the reciprocal of the rate. Therefore, the time it takes for both taps to fill the tank together is 1 / (1/4) = 4 minutes.

This problem has been solved

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