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

Question

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

Bytelearn · Accepted Answer

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. Therefore, when both hoses are working together, they fill 20% + 10% = 30% of the pool in 1 hour.Setting up the inequality: To find out how many hours it would take to fill the pool to over 90% capacity, we can set up the inequality 30% * h > 90%, where h is the number of hours.Solving for h: Now, we need to solve for h. Dividing both sides of the inequality by 30%, we get h > 90% / 30%.Finding the time required: Performing the division, we find that h > 3. This means it takes more than 3 hours to fill the pool to over 90% capacity with both hoses working at the same time.Correct inequality for hours: Looking at the answer choices, the smallest number greater than 3 is 4.5. Therefore, the correct inequality that describes the number of hours, h, it takes to fill the pool to over 90% capacity with both hoses working at the same time is h > 4.5.

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