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Water flows into an empty swimming pool at a constant rate of 50 liter

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rakman123
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Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   28 Jun 2023, 08:03
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Water flows into an empty swimming pool at a constant rate of 50 liters per minute. If the pool's total capacity is 120 cubic meters, approximately how many hours does it take until the pool is filled to 2/3 of its total capacity? (1 liter = 1,000 cubic centimeters)

A. 7
B. 13
C. 27
D. 40
E. 53
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C
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SaquibHGMATWhiz
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   06 Jul 2023, 22:44
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lg800
The cubic centimeter / cubic meter part is throwing me for a loop. Could someone explain how to convert with cubes?

Hey, don't confuse yourself. Take a look at this. We need to convert 80 \(m^3\) to \(cm^3\) here

80 \(m^3=80\times 1m^3\)

\(⇒80\times 1m\times 1m\times 1m\) (Writing \(1m^3=1m\times 1m\times 1m\))

\(⇒80\times 100 cm\times 100 cm\times 100 cm \)

\(⇒80000000cm^3\)
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Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   Updated on: 08 Apr 2024, 06:18
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rakman123
Water flows into an empty swimming pool at a constant rate of 50 liters per minute. If the pool's total capacity is 120 cubic meters, approximately how many hours does it take until the pool is filled to 2/3 of its total capacity? (1 liter = 1,000 cubic centimeters)

A) 7
B) 13
C) 27
D) 40
E) 53
Work done is in terms of m^3 and time taken is to be given in terms of hours. You can convert rate into m^3/hr or work done and time into litres and mins. Converting from a bigger unit to a smaller is easier usually.

\(1 liter = 1,000 cm^3\)

\(Work-done = \frac{2}{3} * 120 m^3 = 80 m*m*m = 80 * 100 cm*100 cm*100 cm = 80 * 1000 * 1000 cm^3 = 80,000 litres\\
\)
\(Time-taken = \frac{80,000}{50} = 1600 mins = \frac{1600}{60} hrs = 26.7\)

Answer (C)­

Check this post for discussion on units conversion: 
https://anaprep.com/arithmetic-unit-conversion/

Originally posted by KarishmaB on 04 Jul 2023, 07:17.
Last edited by KarishmaB on 08 Apr 2024, 06:18, edited 1 time in total.
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   28 Jun 2023, 08:25
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rakman123
Water flows into an empty swimming pool at a constant rate of 50 liters per minute. If the pool's total capacity is 120 cubic meters, approximately how many hours does it take until the pool is filled to 2/3 of its total capacity? (1 liter = 1,000 cubic centimeters)

A) 7
B) 13
C) 27
D) 40
E) 53

Given:

1L = 1000 cubic centimeters

1 meter = 100 cms

1L = \(\frac{1000}{100 * 100 * 100}\) cubic meters = \(10^{-3}\) cubic meter

\(\frac{2}{3}\)rd pools capacity = \(\frac{2}{3} * 120 = 80\) cubic meter

Rate at which water flows = 50 liters per minute = \(50 * 10^{-3}\) cubic meter per minute

Time taken to fill 80 cubic meter = \(\frac{80 }{ 50 * 10^{-3}}\) mintues

Number of hours = \(\frac{80 }{ 50 * 10^{-3}* 60}\)

= \(\frac{80 * 1000}{ 50 * 60}\)

= \(\frac{40 *2}{ 3}\)

= \(40 *\frac{2}{ 3}\)

= \(40 *0.66\)

= 26.66 hours \(\approx 27 \)hours

Option C
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   04 Jul 2023, 05:53
KarishmaB - looping you in for your feedback
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   04 Jul 2023, 15:37
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The cubic centimeter / cubic meter part is throwing me for a loop. Could someone explain how to convert with cubes?
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   13 Jul 2023, 18:22
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rakman123
Water flows into an empty swimming pool at a constant rate of 50 liters per minute. If the pool's total capacity is 120 cubic meters, approximately how many hours does it take until the pool is filled to 2/3 of its total capacity? (1 liter = 1,000 cubic centimeters)

A) 7
B) 13
C) 27
D) 40
E) 53

2/3 of the pool’s capacity is 2/3 × 120 = 80 m³.

time = work/rate

time = (80 m³)/(50 liters/1 min) = (80 m³)(1 min/50 liters)

Since 1 m = 100 cm, it must be true that 1 m³ = 1,000,000 cm³.

So,

time = (80 m³)(1 min/50 liters)(1 liter/1,000 cm³)(1,000,000 cm³/1 m³)

We see that the units of measurement are canceled except for min.

time = 1,600 min

Since 1 h = 60 min, we have:

time = (1,600 min)(1 h/60 min) = 80/3 h ≈ 27 h

Answer: C
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   26 Oct 2023, 16:11
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This one took my mind for a spin lol.
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Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   Updated on: 13 Feb 2024, 18:58
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rakman123
Water flows into an empty swimming pool at a constant rate of 50 liters per minute. If the pool's total capacity is 120 cubic meters, approximately how many hours does it take until the pool is filled to 2/3 of its total capacity? (1 liter = 1,000 cubic centimeters)

A. 7
B. 13
C. 27
D. 40
E. 53

1 meter = \(10^2\) cm
Cubing both sides, we get:
1 cubic meter = \(10^6\) cubic cm

Given conversion rates:
\(10^3\) cubic cm = 1 liter
50 liters = 1 minute

To convert 80 cubic meters -- 2/3 of the pool's capacity -- into hours, we may proceed as follows:

\(\frac{80-cubic-meters}{1} * \frac{10^6-cubic-cm}{1-cubic-meter} * \frac{1-liter}{10^3-cubic-cm} * \frac{1-min}{50-liters} * \frac{1-hour}{60-min} = \frac{800}{5*6} = \frac{80}{3}≈ 27\)

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B
­­

Originally posted by GMATGuruNY on 29 Jan 2024, 09:29.
Last edited by GMATGuruNY on 13 Feb 2024, 18:58, edited 1 time in total.
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   13 Feb 2024, 18:45
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I always find these questions mess me up! The conversions always through me off
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   13 Feb 2024, 23:51
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Jake7Wimmer
I always find these questions mess me up! The conversions always through me off
­
Check out Conversion problems to practice from our Special Questions Directory.

Hope it helps.­
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Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   18 Feb 2024, 11:13
My aaproach was:
50liters per minute is equivalent to 100liters every 2 minutes (1/30 hours).
100liers is 100,000 cubic cm (100 * 1000)
Now, if water flows at 100k cubic cm per 1/30 hour then 1M cubic cm / 1/3 hour.

2/3 of 120 is 80 which is 80M cubic cm
80*1/3 = 80/3 hours.

I found it easier to work with millions­
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Re: Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   09 Aug 2024, 08:53
My 30sec answer approach: Since all answers are upto 2 digits only, Do not let the 10^(whatever value) conversion through you off.

Instead of solving 80,000,000/(50x60), you may solve for 80/(5x6) or 8/3 i.e 2.7 and then convert it into 2 digits by multiplying it with appropriate no of power of 10.
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Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink] Water flows into an empty swimming pool at a constant rate of 50 liter   08 Oct 2024, 18:27
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Attached is a visual that should help.

Note that using the alternative direct proportion formula A1/B1 = A2/B2 is often a better option than the traditional y = kx, which is why I have chosen to use that formula here instead.
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Water flows into an empty swimming pool at a constant rate of 50 liter [#permalink]
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