Math Help −> Puzzles −> AD 2004 state championship logic quiz −> Question 17 −> Answer

Academic Decathlon 2004 State Championship Logic Quiz

Question 17

You need to fill up a bathtub with hot and cold water, but you forgot to put the stopper in the drain. The hot water by itself takes 4.5 minutes to fill the tub with the stopper in the drain. The cold water takes 12 minutes to fill a stoppered tub. Once the tub is full, it takes 18 minutes to drain once the stopper is pulled.

How many minutes will it take to fill the tub using both the hot and cold water, but without the stopper in the drain.

Answer:

Four minutes.

The best way to think of these "work problems" is to consider the number of bathtubs per minute each "worker" (faucet or drain) can complete.

The hot water fills 2/9 bathtubs per minute.

The cold water fills 1/12 bathtubs per minute.

The drain "fills" a negative number, -1/18 bathtubs per minute.

Working together, these three "workers" fill the sum 2/9 + 1/12 - 1/18 bathtubs per minute.

2/9 + 1/12 - 1/18 =
8/36 + 3/36 - 2/36 =
9/36 =
1/4

The result follows.

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