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A swimming pool is filled using four hoses: Hose P and three additio
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07 Aug 2026, 13:18
07 Aug 2026, 13:18
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A swimming pool is filled using four hoses: Hose P and three additional hoses, Q, R , and S , each of which delivers water at \(\frac{2}{3}\) the rate of Hose P . Hose P runs alone until it has filled \(\frac{1}{5}\) of the pool; then hoses Q, R , and S are turned on together with P , and all four run simultaneously until the pool is completely full. What fraction of the time that Hose P alone would take to fill the entire pool does this total process take?
(A) \(\frac{1}{5}\)
(B) \(\frac{4}{15}\)
(C) \(\frac{1}{3} \)
(D) \(\frac{2}{5}\)
(E) \( \frac{7}{15} \)
(A) \(\frac{1}{5}\)
(B) \(\frac{4}{15}\)
(C) \(\frac{1}{3} \)
(D) \(\frac{2}{5}\)
(E) \( \frac{7}{15} \)
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
- Also replying to the unanswered questions
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Re: A swimming pool is filled using four hoses: Hose P and three additio
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13 Aug 2026, 11:06
13 Aug 2026, 11:06
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Explanation
Let Hose P’s rate be 1 pool per unit time.
Hose P alone fills \(\frac{1}{5}\) of the pool in \(\frac{1}{5}\) of the full filling time.
Each of Q, R, S works at \(\frac{2}{3}\) of P’s rate, so together their rate is \(3*\frac{2}{3}\)=2.
With P, all four hoses have total rate \(1+2=3\) times P’s rate.
The remaining \(\frac{4}{5}\) of the pool therefore takes (4/5)/3=\(\frac{4}{15}\) of P’s full filling time.
Total time:
\(\frac{1}{5}+\frac{4}{15}=\frac{3}{15}+\frac{4}{15}=\frac{7}{15}\)
So the total process takes \(\frac{7}{15}\) of the time Hose P alone would need.
Answer: E
Let Hose P’s rate be 1 pool per unit time.
Hose P alone fills \(\frac{1}{5}\) of the pool in \(\frac{1}{5}\) of the full filling time.
Each of Q, R, S works at \(\frac{2}{3}\) of P’s rate, so together their rate is \(3*\frac{2}{3}\)=2.
With P, all four hoses have total rate \(1+2=3\) times P’s rate.
The remaining \(\frac{4}{5}\) of the pool therefore takes (4/5)/3=\(\frac{4}{15}\) of P’s full filling time.
Total time:
\(\frac{1}{5}+\frac{4}{15}=\frac{3}{15}+\frac{4}{15}=\frac{7}{15}\)
So the total process takes \(\frac{7}{15}\) of the time Hose P alone would need.
Answer: E
gmatclubot
Re: A swimming pool is filled using four hoses: Hose P and three additio [#permalink]
13 Aug 2026, 11:06
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