S99-16

Question

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

A. 5 and \(\frac{5}{11}\) minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

Show Answer

Official Answer

C

A. 5 and  \frac{5}{11}  minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

Bunuel · Answer

Official Solution:

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

A. 5 and \(\frac{5}{11}\) minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

Show Answer

Official Answer

C

A. 5 and  \frac{5}{11}  minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

Let  t  stand for the desired time, so that the drain can empty the tub in  t  minutes and faucet Q can fill the tub in  (t - 4)  minutes. Also, the drain does negative work as it empties the tub. The rates for the pipes and the drain are thus
 
P: 1 tub in  10  min   = \frac{1}{10}  tub per min
 
Q: 1 tub in  (t - 4)  min   = \frac{1}{t - 4}  tub per min
 
Drain: -1 tub in  t  min  = -\frac{1}{t}  tub per min
 
Using the fact that all three fixtures together take 6 minutes to fill 1 tub, set up an RTW chart, and use the chart to calculate the total work quantities in the last column.
 Rate (tub/min)  	imes  Time (min)  =  Total Work (tubs) P  \frac{1}{10}   	imes  6  =   \frac{3}{5}  Q  \frac{1}{t - 4}   	imes  6  =   \frac{6}{t - 4}  Drain  \frac{-1}{t}   	imes  6  =   \frac{-6}{t}  Total n/a n/a 1 
Set up an equation summing up the work:
  \frac{3}{5} + \frac{6}{t - 4} - \frac{6}{t} = 1 
 
Multiply by the common denominator,  5t(t - 4) :
  3t(t - 4) + 6(5t) - 6(5)(t - 4) = 5t(t - 4) 
  3t^2 - 12t + 30t - 30t + 120 = 5t^2 - 20t 
  0 = 2t^2 - 8t - 120 
  0 = t^2 - 4t - 60 
  0 = (t - 10)(t + 6) 
 
 t = 10  or  t = -6 
 
The negative value is absurd, so  t = 10 ; the drain can empty the tub in 10 minutes.

Answer: C

VIJAYTHAPLIYAL · Answer

any other quick solution to this.......

Bunuel · Answer

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

A. 5 and \(\frac{5}{11}\) minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

Show Answer

Official Answer

C

A. 5 and  \frac{5}{11}  minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

Let  p  and  q  be the times in minutes needed for faucets P and Q working alone to fill the tub and d be the time in minutes needed for drain to empty the tub.

Given:
Faucet P alone can fill the whole tub in ten minutes -->  p=10 ;
Faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub -->  q=d-4 ;
Faucets P and Q both running and the drain unstopped, the tub fills in six minutes -->  \frac{1}{p}+\frac{1}{q}-\frac{1}{d}=\frac{1}{6}  -->  \frac{1}{10}+\frac{1}{d-4}-\frac{1}{d}=\frac{1}{6}  -->  \frac{1}{d-4}-\frac{1}{d}=\frac{1}{15}  --> substituting the values from the answer choices we'll get  d=10 .

Answer: C.

susig27 · Answer

The question is not clear. The question should be "How long would the drain take to empty the whole tub WHEN BOTH FAUCETS ARE ON". Am I wrong?

Bunuel · Answer

The question is: How long would the drain take to empty the whole tub, when none of the faucets is working? Check solution here: https://gmatclub.com/forum/s99-184744.html#p1752472

carlomereu97 · Answer

You probably are.
maybe you did not thoroughly read the second part of the passage! I am claiming this just 'cause did the same mistake at the beginning. I did the equation considering a "stopped" drain ( so just the combination of the faucets' rates, without considering the drain).
In realty the text says "unstopped" so the equation have to be 
1/x + 1/10 - 1/(4+x) = 1/6
solving it you get x=6 (i considered 1/x the rate of P and 1/(x+4) the drain's rate)
Hope it helps!

PreiteeRanjan · Answer

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

A. 5 and \(\frac{5}{11}\) minutes
B. 6 minutes
C. 10 minutes
D. 19 minutes
E. 30 minutes

Show Answer

Official Answer

C

finding answer from answer choices.

go with the most easy choice that you can handle

always choose LCM method

P takes 10 mins
From the option you take for ex 6(option-b) for drain D
SO Q MUST TAKE 6-4=2 MINS
so now find LCM(10,6,2)=30
FOR MIN P WILL DO 30/10=3(SINCE WORK IS NOT 1 NOW,ITS 30 NOW)
Q=15 WORKS PER MIN
D=5 WORKS/MIN

ALL TOGETHER TOTAL WORK WILL BE =3+15-5=13/MIN.

NOW LOOK 13 WORKS*6 MINS (WHY 6 IS MULTIPLIED,BKZ ITS GIVEN IN THE QN THAT WHEN ALL WORK TOGETHER THEIR WAY IT TAKES 6 MINS TO FEEL THE TANK)
BUT ITS NOT,SO OPTION -B OUT
NEXT OPTION C
P=10
D=10(OPTION)
Q=10-4=6
LCM(10,10,6)=30
PER MIN WORK=3-3+5=5
NOW OUT OF 30 WORKS

IF ALL WORKING THEIR WAY AND 5 IS THE NET WORK PER MINUTE,CAN THEY FEEL THE TANK IN 6 MINUTES?
ANSWER IS YES 5*6=30(TOTAL Capacity as per our lcm work out.

think rethink practice and get the correct choice as dont forget to help for 1 kudo.

Nijssen · Answer

Why can't I get the solution with the combined work formula? T = A*B / A +B
This would be:
(10*(t-4) / (10 + t-4)) - t = 6

ArnoldMagoto · Answer

The easiest solution is to set up the rate equation and plug in the answer choices;

1/10 + 1/t-4 - 1/t = 1/6

Plugging t = 10 gives you 1/6 and that is your correct answer.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

S99-16

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards