wous \( 15 v \) Mox Unit Pretest Subail Ted Ready Toots noto Select the corroct answer, the time if likes the second pump to till the tank when used alone, the situation is reprosertisd by this squation, \( \frac{1}{60}+\frac{1}{y}=\frac{1}{6} \) Ftow fong would it take the second pump, working stone, to sill the tank? A. 75 minutes B. 29 minutes c,' 100 minutes D. 120 minutes

To solve the problem, we need to find the value of \( y \) in the equation: \[ \frac{1}{60} + \frac{1}{y} = \frac{1}{6} \] This equation represents the rates at which two pumps fill a tank. The first pump fills the tank in 60 minutes, and we want to find out how long it takes the second pump to fill the tank alone. ### Step 1: Isolate \(\frac{1}{y}\) First, we can isolate \(\frac{1}{y}\) by subtracting \(\frac{1}{60}\) from both sides: \[ \frac{1}{y} = \frac{1}{6} - \frac{1}{60} \] ### Step 2: Find a common denominator The common denominator for 6 and 60 is 60. We can rewrite \(\frac{1}{6}\) as \(\frac{10}{60}\): \[ \frac{1}{y} = \frac{10}{60} - \frac{1}{60} \] ### Step 3: Perform the subtraction Now, we can perform the subtraction: \[ \frac{1}{y} = \frac{10 - 1}{60} = \frac{9}{60} \] ### Step 4: Simplify the fraction We can simplify \(\frac{9}{60}\): \[ \frac{1}{y} = \frac{3}{20} \] ### Step 5: Take the reciprocal To find \( y \), we take the reciprocal of both sides: \[ y = \frac{20}{3} \] ### Step 6: Convert to minutes Now, we can convert \(\frac{20}{3}\) into minutes: \[ y = 6.67 \text{ minutes} \approx 6 \text{ minutes and } 40 \text{ seconds} \] ### Step 7: Check the options The options provided are: A. 75 minutes B. 29 minutes C. 100 minutes D. 120 minutes Since none of the options match our calculated value, let's convert \( y \) into minutes: \[ y = \frac{20}{3} \text{ minutes} \approx 6.67 \text{ minutes} \] It seems there was a misunderstanding in the interpretation of the problem. Let's solve the equation again to ensure we have the correct interpretation. ### Step 8: Solve the equation again We will solve the equation again to ensure accuracy: \[ \frac{1}{y} = \frac{1}{6} - \frac{1}{60} \] Calculating the right side again: \[ \frac{1}{y} = \frac{10}{60} - \frac{1}{60} = \frac{9}{60} = \frac{3}{20} \] Taking the reciprocal gives: \[ y = \frac{20}{3} \text{ minutes} \] ### Conclusion The second pump takes approximately 6.67 minutes to fill the tank alone, which does not match any of the provided options. It seems there might be a mistake in the options or the interpretation of the problem. Please verify the problem statement or the options provided.