Answer :
To determine which tank is leaking faster, we need to calculate the rate of leakage for each tank. The rate of leakage is the amount of water leaked per minute. Let's calculate the rate for each tank and compare them.
Step 1: Calculate the leakage rate for Tank A
- Tank A leaks [tex]\(\frac{1}{16}\)[/tex] of a gallon in [tex]\(\frac{1}{12}\)[/tex] of a minute.
- To find the leakage rate, we divide the amount of leaked water by the time it took to leak:
[tex]\[
\text{Rate for Tank A} = \frac{\frac{1}{16} \text{ gallon}}{\frac{1}{12} \text{ minute}}
\][/tex]
- To compute this, we multiply [tex]\(\frac{1}{16}\)[/tex] by the reciprocal of [tex]\(\frac{1}{12}\)[/tex]:
[tex]\[
\text{Rate for Tank A} = \frac{1}{16} \times \frac{12}{1} = \frac{12}{16} = 0.75 \text{ gallons per minute}
\][/tex]
Step 2: Calculate the leakage rate for Tank B
- Tank B leaks [tex]\(\frac{3}{80}\)[/tex] of a gallon in [tex]\(\frac{1}{30}\)[/tex] of a minute.
- Similarly, find the leakage rate by dividing the amount leaked by the time:
[tex]\[
\text{Rate for Tank B} = \frac{\frac{3}{80} \text{ gallon}}{\frac{1}{30} \text{ minute}}
\][/tex]
- Multiply [tex]\(\frac{3}{80}\)[/tex] by the reciprocal of [tex]\(\frac{1}{30}\)[/tex]:
[tex]\[
\text{Rate for Tank B} = \frac{3}{80} \times \frac{30}{1} = \frac{90}{80} = 1.125 \text{ gallons per minute}
\][/tex]
Step 3: Compare the leakage rates
- Rate for Tank A: 0.75 gallons per minute
- Rate for Tank B: 1.125 gallons per minute
Since 1.125 gallons per minute is greater than 0.75 gallons per minute, Tank B is leaking faster.
Therefore, Tank B is leaking faster than Tank A.
Step 1: Calculate the leakage rate for Tank A
- Tank A leaks [tex]\(\frac{1}{16}\)[/tex] of a gallon in [tex]\(\frac{1}{12}\)[/tex] of a minute.
- To find the leakage rate, we divide the amount of leaked water by the time it took to leak:
[tex]\[
\text{Rate for Tank A} = \frac{\frac{1}{16} \text{ gallon}}{\frac{1}{12} \text{ minute}}
\][/tex]
- To compute this, we multiply [tex]\(\frac{1}{16}\)[/tex] by the reciprocal of [tex]\(\frac{1}{12}\)[/tex]:
[tex]\[
\text{Rate for Tank A} = \frac{1}{16} \times \frac{12}{1} = \frac{12}{16} = 0.75 \text{ gallons per minute}
\][/tex]
Step 2: Calculate the leakage rate for Tank B
- Tank B leaks [tex]\(\frac{3}{80}\)[/tex] of a gallon in [tex]\(\frac{1}{30}\)[/tex] of a minute.
- Similarly, find the leakage rate by dividing the amount leaked by the time:
[tex]\[
\text{Rate for Tank B} = \frac{\frac{3}{80} \text{ gallon}}{\frac{1}{30} \text{ minute}}
\][/tex]
- Multiply [tex]\(\frac{3}{80}\)[/tex] by the reciprocal of [tex]\(\frac{1}{30}\)[/tex]:
[tex]\[
\text{Rate for Tank B} = \frac{3}{80} \times \frac{30}{1} = \frac{90}{80} = 1.125 \text{ gallons per minute}
\][/tex]
Step 3: Compare the leakage rates
- Rate for Tank A: 0.75 gallons per minute
- Rate for Tank B: 1.125 gallons per minute
Since 1.125 gallons per minute is greater than 0.75 gallons per minute, Tank B is leaking faster.
Therefore, Tank B is leaking faster than Tank A.
