The Malibu Country Club needs to drain its pool for refinishing. The h

volume of pool = 150 * 80 * 10 = 120000 cubic feet
80% of full capacity of pool = 8/10 * 120000 = 96000 cubic feet
rate at which the pool is draining = 60 cubic feet / minute
rate of draining in minutes = 96000 / 60 = 1600 minutes
1600 minutes = 26 hrs 40 minutes
correct answer option B

Rate of draining = 60 cubic/feet

Volume of water in pool = 80*150*10*0.8

Time taken to empty the pool = (80*150*10*0.8)/60

= 1600 minutes or 1600/60

= 26.66 hrs (B)

The amount of water that needs to be drained is:

80 x 150 x 10 x 4/5 = 80 x 150 x 8 = 96,000 ft^3

It will take 96,000/60 = 9600/6 = 1600 minutes or 1600/60 = 80/3 = = 26 2/3 hours to drain the pool.

Answer: B

Volume of water that the pool can hold = (80ft)(150ft)(10ft) = 120000\(ft^{3}\)
Pool is filled to 80% of its current capacity, hence volume of water present in the pool currently = (0.8)(120000\(ft^{3}\)) = 96000\(ft^{3}\)
rate at which hose can drain the pool = 60\(ft^{3}\) per minute
amount of water that can be drained out in 60 minutes i.e. 1 hr = (60\(ft^{3}\))(60) = 3600\(ft^{3}\)
3600\(ft^{3}\) water can be drained out in 1 hr
1\(ft^{3}\) of water can be drained out in \(\frac{1}{3600}\) hrs
96000\(ft^{3}\) of water can be drained out in \(\frac{96000}{3600}\) hrs = \(\frac{80}{3}\) hrs

Excellent opportunity to use UNITS CONTROL, one of the most powerful tools of our method!

\(\frac{{60\,\,{\text{f}}{{\text{t}}^3}}}{{1\,\,\min }}\)

\(\frac{4}{5}\left( {80 \cdot 150 \cdot 10} \right)\,\,\,{\text{f}}{{\text{t}}^3}\,\,\,\,\, \leftrightarrow \,\,\,\,?\,\,{\text{h}}\)

\(?\,\,\, = \,\,\,\frac{4}{5}\left( {80 \cdot 150 \cdot 10} \right)\,\,\,{\text{f}}{{\text{t}}^3}\,\,\,\left( {\frac{{1\,\,\min }}{{60\,\,{\text{f}}{{\text{t}}^3}}}\,\,\begin{array}{*{20}{c}}\\
\nearrow \\ \\
\nearrow \\
\end{array}} \right)\,\,\,\left( {\frac{{1\,\,{\text{h}}}}{{60\,\,\min }}\,\,\begin{array}{*{20}{c}}\\
\nearrow \\ \\
\nearrow \\
\end{array}} \right)\)

Obs.: arrows indicate licit converters.


\(? = \,\,\underleftrightarrow {\frac{{4 \cdot 80 \cdot 150 \cdot 10}}{{5 \cdot 60 \cdot 60}}}\,\, = \,\,\frac{{4 \cdot 8 \cdot 30}}{{6 \cdot 6}} = \frac{{80}}{3} = \frac{{60 + 18 + 2}}{3} = 26\frac{2}{3}\,\,{\text{h}}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Hi All,

We're told that a The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per MINUTE, the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 80% full. We're asked how long it will, in HOURS, to drain the pool. This question is essentially a big 'rate' question, but the answer choices are sufficiently 'spread out' that you can take advantage of them and avoid doing a gigantic calculation.

To start, the current amount of water in the pool is (80)(150)(10)(.8) cubic feet. While that is a lengthy calculation, here's how you can make it easier...

Since we're multiplying 4 numbers together, it does NOT matter what order we do the multiplying... Thus, we can start with (80)(.8) = 64.

(64)(150)(10) = cubic feet of water

The rate of the hose is 60 cubic feet per MINUTE. Notice how 64 is just a bit bigger than 60. Thus, it will take a little more than (150)(10) = 1500 minutes to empty the pool. 1500/60 = 150/6 = 25 hours. Thus, we need answer that is a bit bigger than 25 hours. There's only one answer that matches.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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