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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.
A Jacuzzi tub is filled through two faucets. When filling started, one of the faucets malfunctioned and only one faucet functioned for 4 minutes, before the second one started to work. After the second faucet started to operate it took only 1 more minute to fill the tub. Had the malfunction lasted for 6 minutes, the two faucets would have filled the tub after 20 more seconds of joint operation. How long does it take for the second faucet to fill the tub operating alone?
Between the two situations, the volume of the tub is unchanged, therefore it is an invariant. We use this invariant to set up our equation. Counting the time in minutes (20 s are one third of a minute), we have:
From here, we get:
and we can substitute this value for r in order to find out the volume of the tub in terms of s alone (as a function of s):
But if the second faucet works alone, the volume of the tub is filled in t minutes:
and, therefore, the time in which the second faucet alone can fill the tub is: