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An outdoor pool can be filled to 
20% of its capacity in 1 hour, and 
10% of its capacity in 1 hour by a second hose made by a different manufacturer. Both hoses have a constant rate of flow. Which of the following inequalities describes the number of hours, 
h, it takes to fill the pool to over 
90% capacity with both hoses working at the same time?
Choose 1 answer:
(A) 
h > 3
(B) 
h > 4.5
(c) 
h > 6
(D) 
h > 9

An outdoor pool can be filled to 20% 20 \% of its capacity in 11 hour, and 10% 10 \% of its capacity in 11 hour by a second hose made by a different manufacturer. Both hoses have a constant rate of flow. Which of the following inequalities describes the number of hours, h h , it takes to fill the pool to over 90% 90 \% capacity with both hoses working at the same time?\newlineChoose 11 answer:\newline(A) h>3 \newline(B) h>4.5 \newline(C) h>6 \newline(D) h>9

Full solution

Q. An outdoor pool can be filled to 20% 20 \% of its capacity in 11 hour, and 10% 10 \% of its capacity in 11 hour by a second hose made by a different manufacturer. Both hoses have a constant rate of flow. Which of the following inequalities describes the number of hours, h h , it takes to fill the pool to over 90% 90 \% capacity with both hoses working at the same time?\newlineChoose 11 answer:\newline(A) h>3 h>3 \newline(B) h>4.5 h>4.5 \newline(C) h>6 h>6 \newline(D) h>9 h>9
  1. Determining Combined Filling Rate: Let's determine the combined filling rate of both hoses. The first hose fills 20%20\% of the pool in 11 hour, and the second hose fills 10%10\% of the pool in 11 hour. To find the combined rate, we add these percentages together.\newline20%+10%=30%20\% + 10\% = 30\% per hour.
  2. Finding Hours to Fill 9090% of Pool: Now, we need to find out how many hours it would take to fill more than 9090% of the pool's capacity at this combined rate. We can set up an inequality where the combined rate 30%30\% per hour) multiplied by the number of hours hh is greater than 90%90\%.30\% \times h > 90\%
  3. Setting up the Inequality: To solve for hh, we divide both sides of the inequality by 30%30\%.\newlineh > \frac{90\%}{30\%}
  4. Solving for hh: Performing the division gives us the number of hours.h > 3
  5. Calculating the Number of Hours: Since we are looking for the number of hours it takes to fill the pool to over 90%90\% capacity, we need to choose the answer that reflects "more than 33 hours". Among the given choices, option (A) is correct, h > 3.

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