High School

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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?

Answer :

To determine which tank is leaking faster, we need to find out the rate at which each tank is losing water. We do this by calculating the leak rate for both Tank A and Tank B in gallons per minute. Here’s a step-by-step solution:

1. Tank A:
- Tank A has leaked [tex]\( \frac{1}{16} \)[/tex] of a gallon in [tex]\( \frac{1}{12} \)[/tex] minute.
- To find the rate of leaking in gallons per minute, divide the volume leaked by the time taken:

[tex]\[
\text{Rate for Tank A} = \frac{\frac{1}{16} \text{ gallon}}{\frac{1}{12} \text{ minute}}
\][/tex]

- To simplify the rate, multiply by the reciprocal of time:

[tex]\[
\text{Rate for Tank A} = \frac{1}{16} \times \frac{12}{1} = 0.75 \text{ gallons per minute}
\][/tex]

2. Tank B:
- Tank B has leaked [tex]\( \frac{3}{80} \)[/tex] of a gallon in [tex]\( \frac{1}{30} \)[/tex] minute.
- To find the rate for Tank B, divide the volume leaked by the time taken:

[tex]\[
\text{Rate for Tank B} = \frac{\frac{3}{80} \text{ gallon}}{\frac{1}{30} \text{ minute}}
\][/tex]

- To simplify the rate, multiply by the reciprocal of time:

[tex]\[
\text{Rate for Tank B} = \frac{3}{80} \times \frac{30}{1} = 1.125 \text{ gallons per minute}
\][/tex]

3. Comparison:
- Now compare the leak rates of both tanks:
- Rate for Tank A is 0.75 gallons per minute.
- Rate for Tank B is 1.125 gallons per minute.

4. Conclusion:
- Since 1.125 gallons per minute (Tank B) is greater than 0.75 gallons per minute (Tank A), Tank B is leaking faster.

Thus, the tank that is leaking faster is Tank B.

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada