Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65062

A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
17 Feb 2017, 02:07
Question Stats:
71% (02:40) correct 29% (02:44) wrong based on 225 sessions
HideShow timer Statistics
A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty? A. 12:45pm B. 1:20pm C. 1:40pm D. 2:10pm E. 2:15pm
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Senior Manager
Joined: 19 Apr 2016
Posts: 260
Location: India
GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
17 Feb 2017, 02:34
Bunuel wrote: A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty?
A. 12:45pm B. 1:20pm C. 1:40pm D. 2:10pm E. 2:15pm let the quantity of water in the swimming pool be x so at 7 am it is x and at 9:30 am it is 3x/4 Therefore constant draining rate = 0.25x/150mins At 12 the pool will be half full i.e. x/2 (since x/4 will be drained from 9:30 to 12pm) Also at 12pm the rate gets tripled, new draining rate = (3*0.25x)/150 = 0.75x/150 if 3/4 of the pool is emptied in 150 mins then to empty the remaining half of the pool i.e. x/2 will take t mins. So 0.75x/100 = 0.5x/ t t= (0.5x*150)/0.75x = 100 mins adding 100 mins to 12pm will result in 1:40 pm Hence Option C is correct. Hit Kudos if you liked it



Manager
Joined: 31 Jan 2017
Posts: 56
Location: India
Concentration: Strategy, Leadership
GPA: 4
WE: Project Management (Energy and Utilities)

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
17 Feb 2017, 03:08
Answer : [C]
1/4 emptied in 2.5 hrs. 1/2 emptied in 5 hrs i.e. till 12PM.
draining rate = (1/4) / 2.5 part/hr = 1/10 part/hr increased draining rate = 3/10 part /hr
time taken to drain 1/2 at increased draining rate = (1/2) / (3/10) hrs = 5/3 hrs = 1 hr 40 mins (after 12 PM)



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11043
Location: United States (CA)

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
23 Feb 2017, 09:30
Bunuel wrote: A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty?
A. 12:45pm B. 1:20pm C. 1:40pm D. 2:10pm E. 2:15pm Since 1/4 of the pool was drained between 7 a.m. and 9:30 a.m. (or in 2.5 hours), the rate of drainage was: rate = work/time rate = (1/4)/2.5 = 1/10. From 9:30 a.m. to 12 p.m. (or in another 2.5 hours), the amount of water that was drained was: work = rate x time work = 1/10 x 2.5 = 2.5/10 = 1/4. By 12 p.m. the pool was 3/4  1/4 = 1/2 full. Since the rate tripled after 12 p.m., the new rate is 3/10. Now we can determine how many hours it took to drain the rest of the pool. time = work/rate time = (1/2)/(3/10) = 10/6 = 5/3 = 1⅔ hours = 1 hour and 40 minutes. Thus, the pool was completely empty at 1:40 p.m. Answer: C
_________________
5star rated online GMAT quant self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1339
Location: Malaysia

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
08 Mar 2017, 22:12
Bunuel wrote: A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty?
A. 12:45pm B. 1:20pm C. 1:40pm D. 2:10pm E. 2:15pm Official solution from Veritas Prep. In this Work/Rate problem, you can start by calculating the constant rate. If between 7am and 9:30am the pool drained by \(\frac{1}{4}\) of its capacity, that means that the pool drained at a rate of \(\frac{1}{4}\) pool per 2.5 hours. That then means that the pool drained by \(\frac{1}{10}\) pool per hour during normal hours, and \(\frac{3}{10}\) pool per hour after noon. Since there are 5 hours between 7am and noon, the pool had drained by \(5(\frac{1}{10})\) of its capacity by noon, so it was half full. In the next hour (12pm1pm) it drained by \(\frac{3}{10}\) of its capacity, so by 1pm it had \(\frac{2}{10}\) left to drain. If it drained by \(\frac{3}{10}\) every hour, that means that it only needed \(\frac{2}{3}\) of an hour to finish draining, meaning that it would be done by 1:40pm. Answer choice C is correct.
_________________
"Be challenged at EVERY MOMENT."“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”"Each stage of the journey is crucial to attaining new heights of knowledge."Rules for posting in verbal forum  Please DO NOT post short answer in your post! Advanced Search : https://gmatclub.com/forum/advancedsearch/



Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 513
Location: India

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
09 Mar 2017, 00:09
Let the capacity be 1000. According to the question, 1/4th of the water i.e. 250 got drained in 150 minutes rate =250/150 = 5/3 total time the swimming pool got drained with this rate from 7 am to 12 pm = 5*60 = 300 minutes total water drained = 5/3*300 = 500 left water = 1000  500 = 500 as the rate tripled after 12pm, new rate will be 5/3 *3 = 5 time taken to drain rest of the water with this rate = 500/5 = 100 minutes = 1 hr 40 minutes. hence the swimming pool will get evacuated by 1:40 pm Option C Hit kudos and visit our page for free GMAT prep articles : www.byjus.com/freegmatprep
_________________
GMAT Mentors



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3249
Location: India
GPA: 3.12

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
16 Apr 2018, 23:55
Bunuel wrote: A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty?
A. 12:45pm B. 1:20pm C. 1:40pm D. 2:10pm E. 2:15pm The hotel began draining the swimming pool(which was completely full) at 7 AM. At 9:30 AM(2 hours 30 minutes later), the pool was 3/4th full (or) 1/4th of the pool was drained. At 12:00 PM(2 hours 30 minutes later), working at the same rate, another 1/4th of the pool was drained. Now, the pool was half full at 12 AM. It has been given that the draining rate triples because of evaporation after 12 PM. Initially, 5 hours(300 minutes) was needed to drain the pool to half its capacity, at 3 times the rate, we would be needing \(\frac{300}{3} = 100\) minutes to drain the pool now. Therefore, the pool was completely empty at 1:40 PM(Option C)  100 minutes after 12 PM
_________________
You've got what it takes, but it will take everything you've got



Intern
Joined: 14 Aug 2017
Posts: 14

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
16 May 2020, 00:29
Info that we have > they start at 7 > at 9:30 3/4 is left >> hence 1/4 is drained >> 2 hours 3 mins or 2.5 of an hour = 1/4 >> hence in 5 hours it will drain 1/2 >> hence in 10 hours it will drain 1 >> hence the rate of drain = 1/10
Solve 7 to 12  First 5 hrs @ 1/10 half the pool or 1/2 is drained 12 onwards  The rate triples hence 3*(1/10)
Total drain is > 5 hrs * @ (1/10) + x hrs * @ (1*(3 increased speed)/10) = 1 > (5/10) + (3x/10) = 1 > 10* (5/10) + 10*(3x/10) = 10*1 > 5+ 3x = 10 > 3x = 5 > x = 5/3 *60 > x = 5*20 > x = 100 > x = 1 hour 40 mins



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11043
Location: United States (CA)

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
16 May 2020, 07:50
Bunuel wrote: A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty?
A. 12:45pm B. 1:20pm C. 1:40pm D. 2:10pm E. 2:15pm Solution:Without evaporation, we see that the pool was drained by 1/4 of its capacity in 2.5 = 5/2 hours. Therefore, the drain rate is (1/4)/(5/2) = 2/20 = 1/10. Furthermore, by 12 pm (i.e., in 5 hours), the pool was drained to 1/10 x 5 = 5/10 = 1/2 of its capacity. In other words, the pool was 1/2 full at noon. With evaporation, the new rate is 3/10. So it will take (1/2) / (3/10) = 10/6 = 5/3 = 1 ⅔ = 1 hour 40 minutes more to empty the pool. In other words, the pool will be empty at 1:40 pm. Answer: C
_________________
5star rated online GMAT quant self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



CEO
Joined: 03 Jun 2019
Posts: 3184
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
16 May 2020, 08:00
Bunuel wrote: A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty?
A. 12:45pm B. 1:20pm C. 1:40pm D. 2:10pm E. 2:15pm Given: A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. Asked: If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty? 1/4 of pool was empty in 2.5 hrs Normal rate of draining = x/4*2.5 = x/10 litres/hour; where x is capacity of the pool in litres. In 5 hours, pool drained = (x/10) * 5 = x/2 litres Remaining x/2 pool will be drained in = (x/2) /(3x/10) = 5/3 = 1 2/3 hours = 1 hour 40 mins Pool will be empty at = 12pm + 1 hr 40 min = 1:40pm IMO C
_________________
Kinshook Chaturvedi Email: kinshook.chaturvedi@gmail.com



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6430
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
Show Tags
16 May 2020, 08:34
let total capacity of tank be 4 so from 7 am to 9:30 am ; i.e in 150 mins tank emptied is 1/4 * 4 ; 1 i.e the rate must have been ; 1= rate * 150 ; rate = 1/150 so from 7 am to 12 pm ; i.e 5*60 ; 300 mins tank emptied must be => 1/150*300 ; 2 units so now left with 2 units which would be emptied at thrice rate of 1/150 ; i.e 3 * 1/150 ; 1/50 time taken to empty 2 units at 1/50 rate ; 100 mins i.e 1 hour 40 mins ; so from 12 pm + 1 hour 40 mins ; 1:40 PM OPTION C Bunuel wrote: A hotel began draining its swimming pool at a constant rate at 7am. Beginning at 12pm, the rate tripled because of evaporation. If the pool began completely full and was 3/4 full at 9:30am, at what time was the pool completely empty?
A. 12:45pm B. 1:20pm C. 1:40pm D. 2:10pm E. 2:15pm




Re: A hotel began draining its swimming pool at a constant rate at 7am. Be
[#permalink]
16 May 2020, 08:34




