Question 1197891
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All the responses you have received to now use the same basic method using rate of work -- e.g., the cold water faucet fills the tub in 8 minutes, so it fills 1/8 of the tub in 1 minute.  The method then involves adding fractions with different denominators.<br>
That's a perfectly good method, which you should understand and be able to use.  But there is another method that many students find easier.<br>
Consider the LCM of the two given times.  The LCM of 8 minutes and 12 minutes is 24 minutes.  What could each of the two faucets do in 24 minutes?<br>
The cold water faucet in 24 minutes could fill the tub 24/8 = 3 times; the hot water faucet in 24 minutes could fill the tub 24/12 =2 times.<br>
So in 24 minutes the two faucets together could fill the tub 3+2 = 5 times; that means the number of minutes needed for the two faucets together to fill the one tub is 24/5.<br>
ANSWER: 24/5 minutes, or 4 4/5 minutes, or 4 minutes 48 seconds<br>