We appreciate your visit to Katie and Sunnie both have 20 gallon fish tanks that are leaking water After 15 minutes Katie s tank has leaked tex frac 4 3. 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!
Answer :
Sure, I can help you with that! Here's a detailed, step-by-step solution to determine which fish tank is leaking faster:
1. Find Katie's leak rate:
- Katie's tank has leaked [tex]\( \frac{4}{3} \)[/tex] gallons in 15 minutes.
- To find the leak rate, divide the amount leaked by the time:
[tex]\[
\text{Katie's leak rate} = \frac{\frac{4}{3} \text{ gallons}}{15 \text{ minutes}} = \frac{4}{3} \div 15 = \frac{4}{3} \times \frac{1}{15} = \frac{4}{45} = \frac{8}{90} \approx 0.0889 \text{ gallons per minute}
\][/tex]
2. Find Sunnie's leak rate:
- Sunnie's tank has leaked [tex]\( \frac{3}{4} \)[/tex] gallons in 20 minutes.
- To find the leak rate, divide the amount leaked by the time:
[tex]\[
\text{Sunnie's leak rate} = \frac{\frac{3}{4} \text{ gallons}}{20 \text{ minutes}} = \frac{3}{4} \div 20 = \frac{3}{4} \times \frac{1}{20} = \frac{3}{80} = \frac{6}{160} = \frac{3}{80} \approx 0.0375 \text{ gallons per minute}
\][/tex]
3. Compare the leak rates:
- Katie's leak rate is approximately [tex]\( 0.0889 \)[/tex] gallons per minute.
- Sunnie's leak rate is approximately [tex]\( 0.0375 \)[/tex] gallons per minute.
4. Determine which tank is leaking faster:
- Since [tex]\( 0.0889 \)[/tex] gallons per minute (Katie's leak rate) is greater than [tex]\( 0.0375 \)[/tex] gallons per minute (Sunnie's leak rate), we can conclude that Katie's tank is leaking faster.
Thus, Katie's tank is leaking faster.
1. Find Katie's leak rate:
- Katie's tank has leaked [tex]\( \frac{4}{3} \)[/tex] gallons in 15 minutes.
- To find the leak rate, divide the amount leaked by the time:
[tex]\[
\text{Katie's leak rate} = \frac{\frac{4}{3} \text{ gallons}}{15 \text{ minutes}} = \frac{4}{3} \div 15 = \frac{4}{3} \times \frac{1}{15} = \frac{4}{45} = \frac{8}{90} \approx 0.0889 \text{ gallons per minute}
\][/tex]
2. Find Sunnie's leak rate:
- Sunnie's tank has leaked [tex]\( \frac{3}{4} \)[/tex] gallons in 20 minutes.
- To find the leak rate, divide the amount leaked by the time:
[tex]\[
\text{Sunnie's leak rate} = \frac{\frac{3}{4} \text{ gallons}}{20 \text{ minutes}} = \frac{3}{4} \div 20 = \frac{3}{4} \times \frac{1}{20} = \frac{3}{80} = \frac{6}{160} = \frac{3}{80} \approx 0.0375 \text{ gallons per minute}
\][/tex]
3. Compare the leak rates:
- Katie's leak rate is approximately [tex]\( 0.0889 \)[/tex] gallons per minute.
- Sunnie's leak rate is approximately [tex]\( 0.0375 \)[/tex] gallons per minute.
4. Determine which tank is leaking faster:
- Since [tex]\( 0.0889 \)[/tex] gallons per minute (Katie's leak rate) is greater than [tex]\( 0.0375 \)[/tex] gallons per minute (Sunnie's leak rate), we can conclude that Katie's tank is leaking faster.
Thus, Katie's tank is leaking faster.
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