A reservoir can be filled to (1)/(4) capacity in 1 day by Pump A, and to (1)/(3) capacity in 1 day by Pump B. Both pumps have a constant rate of flow. Which of the following inequalities best describes the number of days, d, it will take for both pumps working at the same time to fill the reservoir to over (7)/(8) capacity? Choose 1 answer: (A) (12)/(7)d (7)/(8) (B) (4)/(d)+(3)/(d) (7)/(8) (D) (d)/(4)+(d)/(3)

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A reservoir can be filled to (1)/(4) capacity in 1 day by Pump A, and to (1)/(3) capacity in 1 day by Pump B. Both pumps have a constant rate of flow. Which of the following inequalities best describes the number of days, d, it will take for both pumps working at the same time to fill the reservoir to over (7)/(8) capacity? Choose 1 answer: (A) (12)/(7)d > (7)/(8) (B) (4)/(d)+(3)/(d) <= (7)/(8) (C) (7)/(12)d > (7)/(8) (D) (d)/(4)+(d)/(3) <= (7)/(8) ar equations word problems | Lesson

Bytelearn · Accepted Answer

Calculate Combined Rate: Let's determine the combined rate of both pumps working together. Pump A fills (1)/(4) of the reservoir in 1 day, and Pump B fills (1)/(3) of the reservoir in 1 day. To find the combined rate, we add these fractions together. Combined rate = (1)/(4) + (1)/(3) To add fractions, we need a common denominator, which is 12 in this case. Combined rate = (3)/(12) + (4)/(12) Combined rate = (7)/(12) This means that together, the pumps can fill (7)/(12) of the reservoir in 1 day.Set Up Inequality: Now, let's set up an inequality to find the number of days, d, it takes to fill more than (7)/(8) of the reservoir's capacity. (7)/(12)d > (7)/(8) We want to solve for d.Isolate Variable: To solve the inequality, we need to isolate d. We can do this by multiplying both sides of the inequality by the reciprocal of (7)/(12), which is (12)/(7). d > (7)/(8) * (12)/(7)Simplify Inequality: Now, we simplify the right side of the inequality by canceling out the 7s. d > (12)/(8) d > (3)/(2) d > 1.5 This means it will take more than 1.5 days for both pumps to fill the reservoir to over (7)/(8) capacity.Match with Answer Choices: Looking at the answer choices, we need to find the one that matches our inequality. The correct inequality should represent that more than 1.5 days are needed to fill over (7)/(8) of the reservoir. (A) (12)/(7)d > (7)/(8) - This is the inequality we derived, but it's not simplified. (B) (4)/(d)+(3)/(d) <= (7)/(8) - This is incorrect because it suggests the sum of the reciprocals of the days, which doesn't make sense in this context. (C) (7)/(12)d > (7)/(8) - This is the inequality we started with, which is correct. (D) (d)/(4)+(d)/(3) <= (7)/(8) - This is incorrect because it suggests the sum of the days divided by the rates, which is not the correct representation of the combined rate.

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