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# A pump started filling an empty pool with water and continue

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A pump started filling an empty pool with water and continue [#permalink]  20 Nov 2008, 10:30
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A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and $$1\frac{1}{4}$$ hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

A. $$2\frac{1}{3}$$
B. $$2\frac{2}{3}$$
C. 3
D. $$3\frac{1}{2}$$
E. $$3\frac{2}{3}$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Apr 2014, 02:29, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: pump--25 [#permalink]  20 Nov 2008, 22:18
Jcpenny wrote:
A pump started filling an empty pool with water and continued at
a constant rate until the pool was full. At noon the pool was 1/3 full,
and 1+1/4 hours later it was 3/4 full. What was the total number of
hours that it took the pump to fill the pool?
A. 2+1/3 B. 2+2/3 C. 3
D. 3+1/2 E. 3+2/3

in 1+1/4 =5/4 hrs the pump filled 3/4-1/3 = 5/12th of the pool
in 1 hr it fills 1/3 of the pool
so in 3 hrs it will fill the entire pool.
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Re: pump--25 [#permalink]  10 Apr 2014, 16:22
alpha_plus_gamma wrote:
Jcpenny wrote:
A pump started filling an empty pool with water and continued at
a constant rate until the pool was full. At noon the pool was 1/3 full,
and 1+1/4 hours later it was 3/4 full. What was the total number of
hours that it took the pump to fill the pool?
A. 2+1/3 B. 2+2/3 C. 3
D. 3+1/2 E. 3+2/3

in 1+1/4 =5/4 hrs the pump filled 3/4-1/3 = 5/12th of the pool
in 1 hr it fills 1/3 of the pool
so in 3 hrs it will fill the entire pool.

I was with you up until 5/12th of the pool. How did you get the in 1 hour it fills 1/3 of the poor?
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Re: A pump started filling an empty pool with water and [#permalink]  10 Apr 2014, 19:13
Expert's post
Jcpenny wrote:
A pump started filling an empty pool with water and continued at
a constant rate until the pool was full. At noon the pool was 1/3 full,
and 1+1/4 hours later it was 3/4 full. What was the total number of
hours that it took the pump to fill the pool?
A. 2+1/3 B. 2+2/3 C. 3
D. 3+1/2 E. 3+2/3

The time elapsed between 1/3 full pool and 3/4 full pool is 5/4 hrs. This means 3/4 - 1/3 = 5/12 of the pool was filled in 5/4 hrs.

Again, (5/12)th of the pool will be filled in 5/4 hrs

1 pool will be filled in $$\frac{5/4}{5/12} * 1 = 3$$ hrs
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Re: A pump started filling an empty pool with water and continue [#permalink]  12 Apr 2015, 21:07
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A pump started filling an empty pool with water and continue [#permalink]  02 Jun 2015, 06:04
Jcpenny wrote:
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and $$1\frac{1}{4}$$ hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

A. $$2\frac{1}{3}$$
B. $$2\frac{2}{3}$$
C. 3
D. $$3\frac{1}{2}$$
E. $$3\frac{2}{3}$$

Taking a smart number.
Let the capacity of the pool be 12 Liters

At 12 PM = $$\frac{1}{3}*12$$ = 4 Liters of water was in the pool.
After $$1\frac{1}{4}$$ Hours i.e. at 13:15 Hrs = $$\frac{3}{4}*12$$ = 9 liters of water was in the pool.

So in 75 mins the pump fills 9-4 = 5 liters of water in the pool.

setting up ratio and proportion

$$\frac{X}{75}=\frac{12}{5}$$
$$X = 180 mins = 3 Hours$$

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Re: A pump started filling an empty pool with water and continue [#permalink]  02 Jun 2015, 07:54
Expert's post
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and 1 1/4 hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

(3/4) - (1/3) = 5/12. 5/12 of the pool was full in 1 1/4 hours time (5/4 hours). To determine a rate of filling we divide how much is full by the time. That is (5/12) ÷ (5/4) = 1/3. This means it fills a pool in 3 hours.

A. 2 1/3
B. 2 2/3
C. 3
D. 3 1/2
E. 3 2/3
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Re: A pump started filling an empty pool with water and continue   [#permalink] 02 Jun 2015, 07:54
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