Question 1192357: A water tank can be filled in 9 hours and then drained in 12 hours. How long would it take to fill the water tank if the drain is left open? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52781) (Show Source):
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A water tank can be filled in 9 hours and then drained in 12 hours.
How long would it take to fill the water tank if the drain is left open?
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Filling rate is of the tank volume per hour.
Draining rate is of the tank volume per hour.
The net filling rate is the difference = = .
Hence, the tank will be filled in 36 hours, if the drain is left open.
The other tutor showed a standard algebraic method for solving this kind of "working together" problem.
Here is an alternative you might try that many students like because it avoids solving equations with fractions.
Consider the least common multiple of the two given times, which is 36 hours.
In 36 hours, the number of tanks that could be filled is 36/9 = 4; in 36 hours the number of tanks that could be drained is 36/12 = 3. So in 36 hours the net would be filling the tank 4-3 = 1 time.
