It takes Tap A 12 minutes to fill a container measuring 8 cm by 10 cm by 18 cm completely while it takes Tap B 15 minutes. How long will it take to completely fill the container with water if both the taps are turned on at the same time and 4 cubic cups of edges 3 cm, filled with water, are poured into the container? Leave your answer in minutes and round off to 2 decimal places.
Question
It takes Tap A 12 minutes to fill a container measuring 8 cm by 10 cm by 18 cm completely while it takes Tap B 15 minutes. How long will it take to completely fill the container with water if both the taps are turned on at the same time and 4 cubic cups of edges 3 cm, filled with water, are poured into the container? Leave your answer in minutes and round off to 2 decimal places.
Solution
Sure, let's break this down step by step.
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First, we need to find the volume of the container. The volume of a rectangular prism (which is what this container is) is found by multiplying its length, width, and height. So, the volume of the container is 8 cm * 10 cm * 18 cm = 1440 cubic cm.
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Next, we need to find the rate at which each tap fills the container. Tap A fills the container in 12 minutes, so its rate is 1440 cubic cm / 12 minutes = 120 cubic cm/minute. Tap B fills the container in 15 minutes, so its rate is 1440 cubic cm / 15 minutes = 96 cubic cm/minute.
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If both taps are turned on at the same time, they will fill the container at a combined rate of 120 cubic cm/minute + 96 cubic cm/minute = 216 cubic cm/minute.
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Now, we need to account for the 4 cubic cups of water that are already in the container. Each cup has edges of 3 cm, so its volume is 3 cm * 3 cm * 3 cm = 27 cubic cm. Four cups would therefore have a volume of 4 * 27 cubic cm = 108 cubic cm.
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Subtracting this from the total volume of the container, we find that the taps need to fill 1440 cubic cm - 108 cubic cm = 1332 cubic cm.
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Finally, we divide this volume by the combined rate of the taps to find the time it will take to fill the container: 1332 cubic cm / 216 cubic cm/minute = 6.17 minutes.
So, it will take approximately 6.17 minutes to fill the container if both taps are turned on at the same time and 4 cubic cups of water are already in the container.
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