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MMLU-Pro / 7779 / Your swimming pool containing 60,000 gal of water has been contaminated by …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Your swimming pool containing 60,000 gal of water has been contaminated by $5 \mathrm{~kg}$ of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of 200gal/min200 \mathrm{gal} / \mathrm{min}. Find the time TT at which the concentration of dye first reaches the value $0.02 \mathrm{~g} / \mathrm{gal}$.
Plain-text mathematical notation (without MathML)
Your swimming pool containing 60,000 gal of water has been contaminated by $5 \mathrm{~kg}$ of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of 200gal/min. Find the time T at which the concentration of dye first reaches the value $0.02 \mathrm{~g} / \mathrm{gal}$.
Original LaTeX notation
Your swimming pool containing 60,000 gal of water has been contaminated by $5 \mathrm{~kg}$ of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of $200 \mathrm{gal} / \mathrm{min}$. Find the time $T$ at which the concentration of dye first reaches the value $0.02 \mathrm{~g} / \mathrm{gal}$.

category

math

options

  1. 10.250 hours
  2. 7.550 hours
  3. 6.000 hours
  4. 6.875 hours
  5. 8.255 hours
  6. 9.100 hours
  7. 7.136 hour
  8. 8.670 hours
  9. 5.320 hours
  10. 7.780 hours

src

scibench-diff

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Source and history

upstream_id / Original problem ID
7779
task_id
d9c8b5b9-c1c2-5bc3-83d0-5dd8c661d877
task_key
default--test--7779
task_revision_id
1
config / split
default / test

Official source

initial import