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In one minute, A will fill 1/8 of the cooler.
Meanwhile, B will fill 1/12 of the cooler in one minute.
Let's put them in a common denominator:
1/8 * 12 = 12/96
1/12 * 8 = 8/96
12/96 + 8/96 = 20/96, which simplifies down to 5/24.
So the combined faucets are getting 5/24th of the cooler filled per minute. After four minutes they will have filled 20/4ths fo the cooler, and they will have finished before the end of the fifth minute. To be specific, in one minute they would fill 5/24ths of the cooler, but only have 4 more to fill, so only 4/5 of the last minute is used.
One cooler divided by a rate of 5/24 per minute gives us 4.8, or 4 and 4/5 of a minute to fill the cooler exactly, which matches what we had above.
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