A full 1,500-liter water tank springs a leak and is losing 2 liters per minute. A second tank has 300 liters and is being filled at a rate of 6 liters per minute.

Determine if the following statement is true or false:

Both tanks will have the same amount of water after a certain period of time.

a) True
b) False

The leak rate from the first tank is faster than the fill rate of the second tank. Thus, the first tank will empty before the second tank reaches its capacity. a) True

Explanation:

The first tank has a capacity of 1,500 liters and is losing 2 liters per minute. To determine if this tank will eventually empty, we need to calculate the time it takes for it to run out of water.

Step 1: Calculate the time it takes for the first tank to empty:

Time (minutes) = Tank Capacity / Leak Rate

Time = 1,500 liters / 2 liters per minute = 750 minutes

So, it will take 750 minutes for the first tank to empty.

Step 2: Calculate the amount of water added to the second tank in 750 minutes:

Amount of water added = Fill Rate x Time

Amount of water added = 6 liters per minute x 750 minutes = 4,500 liters

Step 3: Determine if the second tank will fill up before the first tank empties:

The second tank has a capacity of 300 liters, and we have calculated that it will have 4,500 liters added to it in 750 minutes. Since 4,500 liters is greater than the capacity of the second tank (300 liters), it will fill up before the first tank empties.

Therefore, the statement "a) True" is correct. The second tank will fill up before the first tank empties.

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