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.
### 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.
