two pumps were required to pump the water out of a submerged area after a hurricane. pump a, the larger of the two pumps, can pump the water out in 24 hours, whereas it would take pump b 120 hours. both pumps were working for the first 6 hours until pump a broke down. how long did it take pump b to pump out the remaining water?

pump b pumped alone for hours.

Question

two pumps were required to pump the water out of a submerged area after a hurricane. pump a, the larger of the two pumps, can pump the water out in 24 hours, whereas it would take pump b 120 hours. both pumps were working for the first 6 hours until pump a broke down. how long did it take pump b to pump out the remaining water?

pump b pumped alone for hours.

pump b pumped alone for   hours.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Work Rate Problems" ], "new_concepts": [], "current_concepts": [ "Work Rate Problems", "Rational Equations" ] } ## Calculate the combined work rate and work completed in the first 6 hours $$ \begin{aligned} R_A &= \frac{1}{24} \ R_B &= \frac{1}{120} \ R_{\text{combined}} &= \frac{1}{24} + \frac{1}{120} = \frac{5}{120} + \frac{1}{120} = \frac{6}{120} = \frac{1}{20} \ W_{\text{initial}} &= R_{\text{combined}} \times 6 = \frac{1}{20} \times 6 = \frac{3}{10} \end{aligned} $$ ## Determine the remaining work to be done $$ W_{\text{remaining}} = 1 - \frac{3}{10} = \frac{7}{10} $$ ## Calculate the time required for Pump B to complete the remaining work alone $$ \begin{aligned} t_B &= \frac{W_{\text{remaining}}}{R_B} \ t_B &= \frac{\frac{7}{10}}{\frac{1}{120}} = \frac{7}{10} \times 120 = 84 \end{aligned} $$ Two pumps were required to pump the water out of a submerged area after a hurricane. Pump A, the larger of the two pumps, can pump the water out in 24 hours, whereas it would take pump B 120 hours. Both pumps were working for the first 6 hours until pump A broke down. How long did it take pump B to pump out the remaining water? Pump B pumped alone for 84 hours. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Work Rate Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the combined work rate and work completed in the first 6 hours

Determine the remaining work to be done

Calculate the time required for Pump B to complete the remaining work alone

Answer: