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
Q. 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
Determining Combined Filling Rate: Let's determine the combined filling rate of both hoses. The first hose fills 20% of the pool in 1 hour, and the second hose fills 10% of the pool in 1 hour. To find the combined rate, we add these percentages together.20%+10%=30% per hour.
Finding Hours to Fill 90% of Pool: Now, we need to find out how many hours it would take to fill more than 90% of the pool's capacity at this combined rate. We can set up an inequality where the combined rate 30% per hour) multiplied by the number of hours h is greater than 90%.30\% \times h > 90\%
Setting up the Inequality: To solve for h, we divide both sides of the inequality by 30%.h > \frac{90\%}{30\%}
Solving for h: Performing the division gives us the number of hours.h > 3
Calculating the Number of Hours: Since we are looking for the number of hours it takes to fill the pool to over 90% capacity, we need to choose the answer that reflects "more than 3 hours". Among the given choices, option (A) is correct, h > 3.
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