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Two water tanks are leaking. Tank [tex]$A$[/tex] has leaked [tex]$\frac{1}{16}$[/tex] of a gallon in [tex]$\frac{1}{12}$[/tex] minute, and Tank [tex]$B$[/tex] has leaked [tex]$\frac{3}{80}$[/tex] of a gallon in [tex]$\frac{1}{30}$[/tex] minute. Which tank is leaking faster?

Select the correct answer from the drop-down menu to complete the sentence.

Tank __________ leaks faster.

Answer :

To determine which tank is leaking faster, we need to compare the rates at which each tank is leaking in gallons per minute. Here is a step-by-step solution:

### Step 1: Understanding the Problem
- Tank A has leaked [tex]\(\frac{1}{16}\)[/tex] of a gallon in [tex]\(\frac{1}{12}\)[/tex] minute.
- Tank B has leaked [tex]\(\frac{3}{80}\)[/tex] of a gallon in [tex]\(\frac{1}{30}\)[/tex] minute.
- We need to find the rate of leakage for each tank and compare them.

### Step 2: Calculating the Leak Rate for Tank A
The rate of leakage can be found by dividing the amount leaked by the time taken.
- Amount leaked by Tank A: [tex]\(\frac{1}{16}\)[/tex] gallons
- Time taken by Tank A: [tex]\(\frac{1}{12}\)[/tex] minute

The leakage rate for Tank A:
[tex]\[
\text{Rate for Tank A} = \left(\frac{1}{16} \text{ gallons}\right) \div \left(\frac{1}{12} \text{ minute}\right)
\][/tex]
To divide by a fraction, you multiply by its reciprocal:
[tex]\[
\text{Rate for Tank A} = \left(\frac{1}{16}\right) \times \left(\frac{12}{1}\right) = \frac{12}{16} = 0.75 \text{ gallons per minute}
\][/tex]

### Step 3: Calculating the Leak Rate for Tank B
The rate of leakage can be found similarly:
- Amount leaked by Tank B: [tex]\(\frac{3}{80}\)[/tex] gallons
- Time taken by Tank B: [tex]\(\frac{1}{30}\)[/tex] minute

The leakage rate for Tank B:
[tex]\[
\text{Rate for Tank B} = \left(\frac{3}{80} \text{ gallons}\right) \div \left(\frac{1}{30} \text{ minute}\right)
\][/tex]
[tex]\[
\text{Rate for Tank B} = \left(\frac{3}{80}\right) \times \left(\frac{30}{1}\right) = \frac{90}{80} = 1.125 \text{ gallons per minute}
\][/tex]

### Step 4: Comparing the Leak Rates
- Leakage rate of Tank A: 0.75 gallons per minute
- Leakage rate of Tank B: 1.125 gallons per minute

Since 1.125 is greater than 0.75, Tank B is leaking faster.

### Conclusion:
Tank B leaks faster.

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