High School

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 water tank is leaking faster, we need to calculate the rate of leakage for each tank and compare them.

1. Calculate the leakage rate for Tank A:
- Tank A has leaked [tex]\(\frac{1}{16}\)[/tex] of a gallon in [tex]\(\frac{1}{12}\)[/tex] of a minute.
- To find the leakage rate, divide the amount leaked by the time taken:
[tex]\[
\text{Rate for Tank A} = \frac{\frac{1}{16}}{\frac{1}{12}} = \frac{1}{16} \times \frac{12}{1} = \frac{12}{16} = 0.75 \text{ gallons per minute}
\][/tex]

2. Calculate the leakage rate for Tank B:
- Tank B has leaked [tex]\(\frac{3}{80}\)[/tex] of a gallon in [tex]\(\frac{1}{30}\)[/tex] of a minute.
- Similarly, divide the amount leaked by the time taken:
[tex]\[
\text{Rate for Tank B} = \frac{\frac{3}{80}}{\frac{1}{30}} = \frac{3}{80} \times \frac{30}{1} = \frac{90}{80} = 1.125 \text{ gallons per minute}
\][/tex]

3. Compare the leakage rates:
- The leakage rate for Tank A is 0.75 gallons per minute.
- The leakage rate for Tank B is 1.125 gallons per minute.

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

Therefore, Tank B is the faster leaking tank.

Other Questions