Answer :
To solve this problem, we need to determine how fast the sink and the shower leak water per minute and then compare these rates.
1. Sink Leak Rate:
- The sink leaks [tex]\(\frac{1}{3}\)[/tex] of a cup every 5 minutes.
- To find the leak rate per minute, divide the amount leaked by the time it takes:
[tex]\[
\text{Sink leak per minute} = \frac{1}{3} \div 5 = \frac{1}{3} \times \frac{1}{5} = \frac{1}{15}
\][/tex]
- This means the sink leaks [tex]\(\frac{1}{15}\)[/tex] of a cup per minute, which is approximately 0.067 cups per minute.
2. Shower Leak Rate:
- The shower leaks [tex]\(\frac{2}{5}\)[/tex] of a cup every 8 minutes.
- To find the leak rate per minute, divide the amount leaked by the time it takes:
[tex]\[
\text{Shower leak per minute} = \frac{2}{5} \div 8 = \frac{2}{5} \times \frac{1}{8} = \frac{2}{40} = \frac{1}{20}
\][/tex]
- This means the shower leaks [tex]\(\frac{1}{20}\)[/tex] of a cup per minute, which is 0.05 cups per minute.
3. Comparing the Leak Rates:
- The sink leaks approximately 0.067 cups per minute, while the shower leaks 0.05 cups per minute.
- Clearly, the sink leaks faster because 0.067 is greater than 0.05.
4. Difference in Leak Rates:
- To find the difference between the leak rates, subtract the shower's leak rate from the sink's leak rate:
[tex]\[
\text{Difference} = 0.067 - 0.05 = 0.017
\][/tex]
- The difference in leak rates is approximately 0.017 cups per minute.
In summary:
- Sink leaks 0.067 cups per minute.
- Shower leaks 0.05 cups per minute.
- The sink leaks faster.
- The difference in leak rates is 0.017 cups per minute.
1. Sink Leak Rate:
- The sink leaks [tex]\(\frac{1}{3}\)[/tex] of a cup every 5 minutes.
- To find the leak rate per minute, divide the amount leaked by the time it takes:
[tex]\[
\text{Sink leak per minute} = \frac{1}{3} \div 5 = \frac{1}{3} \times \frac{1}{5} = \frac{1}{15}
\][/tex]
- This means the sink leaks [tex]\(\frac{1}{15}\)[/tex] of a cup per minute, which is approximately 0.067 cups per minute.
2. Shower Leak Rate:
- The shower leaks [tex]\(\frac{2}{5}\)[/tex] of a cup every 8 minutes.
- To find the leak rate per minute, divide the amount leaked by the time it takes:
[tex]\[
\text{Shower leak per minute} = \frac{2}{5} \div 8 = \frac{2}{5} \times \frac{1}{8} = \frac{2}{40} = \frac{1}{20}
\][/tex]
- This means the shower leaks [tex]\(\frac{1}{20}\)[/tex] of a cup per minute, which is 0.05 cups per minute.
3. Comparing the Leak Rates:
- The sink leaks approximately 0.067 cups per minute, while the shower leaks 0.05 cups per minute.
- Clearly, the sink leaks faster because 0.067 is greater than 0.05.
4. Difference in Leak Rates:
- To find the difference between the leak rates, subtract the shower's leak rate from the sink's leak rate:
[tex]\[
\text{Difference} = 0.067 - 0.05 = 0.017
\][/tex]
- The difference in leak rates is approximately 0.017 cups per minute.
In summary:
- Sink leaks 0.067 cups per minute.
- Shower leaks 0.05 cups per minute.
- The sink leaks faster.
- The difference in leak rates is 0.017 cups per minute.
