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Worked example

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Combined Work Rates

A public work-rate question that shows why individual completion times must be converted to rates before combining two workers.

Question

Working alone, Pump A fills an empty reservoir in 66 hours and Pump B fills the same reservoir in 1010 hours. Running together from empty, how many hours do the two pumps need to fill the reservoir?

  1. a.3.753.75 hours
  2. b.88 hours
  3. c.1515 hours
  4. d.1616 hours

Correct answer

A. 3.753.75 hours

Full reasoning

  1. 1Convert each completion time to a rate: Pump A fills 16\tfrac{1}{6} of the reservoir per hour and Pump B fills 110\tfrac{1}{10} per hour.
  2. 2Add the rates because the pumps work simultaneously: 16+110=530+330=830=415\tfrac{1}{6} + \tfrac{1}{10} = \tfrac{5}{30} + \tfrac{3}{30} = \tfrac{8}{30} = \tfrac{4}{15} reservoir per hour.
  3. 3Invert the combined rate to get the time for one full reservoir: 154=3.75\tfrac{15}{4} = 3.75 hours.

Why each choice is right or wrong

Choice A

Correct. The combined rate is 16+110=830=415\tfrac{1}{6} + \tfrac{1}{10} = \tfrac{8}{30} = \tfrac{4}{15} reservoir per hour, so the time is 154=3.75\tfrac{15}{4} = 3.75 hours.

Choice B

This averages the two completion times, but times cannot be averaged; only the per-hour rates combine additively.

Choice C

This divides 6×10=606 \times 10 = 60 by the difference of the times, 10−6=410 - 6 = 4, mixing up the together-work setup with an overtake-style calculation.

Choice D

This adds the two completion times, which would only make sense if the pumps ran one after the other and each filled the reservoir entirely.

Related formula

Combined work time from individual times

1T=1tA+1tB\frac{1}{T} = \frac{1}{t_A} + \frac{1}{t_B}

Assumptions: Both workers run simultaneously at constant rates without interfering with each other.

Related topic and practice

Rates, Work, and MixturesDilution MixturesSuccessive percentage changesCreate a free account to practice

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Sources

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. Prealgebra 2e, Section 5.6: Ratios and Rate — OpenStax. Accessed 2026-07-11. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.
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Sources and corrections

Sources last checked 2026-08-07

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