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Difficulty: EasyWork Rate and Combined Work

Pump A can fill a water storage tank in 44 hours when operating alone at a constant rate. Pump B can fill the same tank in 66 hours when operating alone at a constant rate. If both pumps operate simultaneously at their respective constant rates, how many hours will it take to fill the empty tank completely?

  1. 2.42.4 hoursAnswer
  2. B
    5.05.0 hours
  3. C
    10.010.0 hours
  4. D
    2.02.0 hours
  5. E
    512\frac{5}{12} hours

Answer

2.42.4 hours
To find the combined time, sum the hourly rates of both pumps: 14+16=512\frac{1}{4} + \frac{1}{6} = \frac{5}{12} tanks per hour. Inverting this combined rate gives the total hours required: 125=2.4\frac{12}{5} = 2.4 hours.

Step-by-Step Solution

1
Determine individual work rates per hour.
Pump A's rate is 14\frac{1}{4} of the tank per hour, and Pump B's rate is 16\frac{1}{6} of the tank per hour.
Work rate is defined as Rate=WorkTime\text{Rate} = \frac{\text{Work}}{\text{Time}}.
2
Add the individual rates to find the combined rate.
\text{Combined Rate} = \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}\text{ tank per hour}.
When entities work together, their work rates add linearly.
3
Calculate the total time required for the combined rate to complete 11 full tank.
\text{Time} = \frac{1}{\text{Combined Rate}} = \frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4\text{ hours}.
Time equals total work divided by the combined work rate.

Key Concept

Combined Work Rate Formula
Estimated Time:1m 0s
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Topics

Work Rate and Combined Work

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