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

Question

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

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

SaquibHGMATWhiz · Accepted Answer

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	imes 1m^3

⇒80	imes 1m	imes 1m	imes 1m  (Writing  1m^3=1m	imes 1m	imes 1m )

⇒80	imes 100 cm	imes 100 cm	imes 100 cm

⇒80000000cm^3

KarishmaB · Answer

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/

gmatophobia · Answer

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

rakman123 · Answer

KarishmaB  - looping you in for your feedback

lg800 · Answer

The cubic centimeter / cubic meter part is throwing me for a loop. Could someone explain how to convert with cubes?

JeffTargetTestPrep · Answer

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

averagedude23 · Answer

This one took my mind for a spin lol.

GMATGuruNY · Answer

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

B

Jake7Wimmer · Answer

I always find these questions mess me up! The conversions always through me off

Bunuel · Answer

Check out  Conversion problems  to practice from our  Special Questions Directory .

Hope it helps.

ruis · Answer

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

nikchau · Answer

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.

mcelroytutoring · Answer

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.

Dbrunik · Answer

100*100*100*80=80,000,000

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

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

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