Official Solution:

If Samson is filling a bathtub with COLD water, it will take him 6 minutes and 40 seconds, and if he fills it with HOT water, it will take him 8 minutes. If draining the tub takes 13 minutes and 20 seconds, how many minutes will it take to fill up the bath tub with both HOT and COLD water running while the plug is out, so the water is constantly draining?

A. 16
B. 12
C. 8.6
D. 5
E. 4.75


Measure the speeds in tubs per second:
\(Cold = \frac{1}{400}\)
\(Hot = \frac{1}{480}\)
\(Drain = \frac{1}{800}\)
The net speed is:
\(\frac{12}{4800} + \frac{10}{4800} - \frac{6}{4800} = \frac{16}{4800} = \frac{1}{300}\)

The answer is therefore 300 seconds, or 5 minutes.


Answer: D
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D is the answer. Used the same approached as suggested by Bunuel. Got the answer in less than 2 min. Thanks

I did not get the solution , could you please explain in detail

You should indicate what was unclear in the solution. Anyway, you can check alternative solutions here: if-samson-is-filling-a-bathtub-with-cold-water-it-will-take-92416.html

Hope it helps.
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I think this is a high-quality question and I agree with explanation. Should state that COLD and HOT water are coming from different pipes and tanks. The way it is written it is not clear if the water is coming out of the same pipe (as is the case for the modern American bathtub). I averaged the speed to 7 minutes and 20 seconds for COLD and HOT and got stuck. I would have gotten the answer right if the problem specified that the COLD and HOT water come from 2 independent separate pipes.

I think this is a poor-quality question. Question tries to confer that the hot+cold rates are additive. However, this is not necessarily what one would intuitively think: when I turn a mixture of hot/cold water on in any bathtub I've used, the water is, say, synthesized thus I thought the fill rate would be somewhere between hot and cold fill up time.

I think this is a poor-quality question and I agree with explanation. Doesn't seem like a 700 level problem.

since we are talking about seconds I took the numerator as 60 & not 1

CW 60/400
HW 60/480
Drain 60/800

so
120/800+100/800-60/800
220-60/800
160/800
1/5
so 5 mins

experts please comment if the bold part approach is correct

Faster way of doing this Question is by using smaller fractions:

CW= 6m 40 secs = 6[2][/3]= 20/3
HW= 8m = 8
Drain= 13m 20secs= 13[1][/3]= 40/3

So, we get:

1/ Total Time= 3/20 + 1/8 - 3/40
= (6+5-3)/40
= 1/5

Hence, Total time= 5 mins

How did you calculate the net speed?

Would be helpful to clarify the language used in the question.

- Indicate that cold water is supplied by one pipe and that hot water is supplied by a separate pipe and that these are different operations.

- The phrase "while the plug is out" may be confusing. It could be substituted with "unplugged".

Hello Bunuel,


Where did I falter?

Below is my approach:

CW= 6m 40 secs = 6[2][/3]= 20/3
HW= 8m = 8
Drain= 13m 20secs= 13[1][/3]= 40/3

Multiplying the above numbers by 3

CW=20, HW=24, Drain=40

Let work done= LCM( 20,24,40)= 120 UNITS

Rate of CW= 6 units/ min ,Rate of HW= 5 units/min, Rate of draining pipe= negative(3 units/min)

Combined rate by all 3 pipes in one min= 6+5-3= 8 units/ min

so 3 pipes together fill 8 units in a min. For 120 units they take 15 mins. - did not find the option in answer choices, selected 16.

I multiplied the numbers by 3 earlier. Should the final answer be divided by same number to arrive at the correct answer? Is that some sort of a mathematical rule?
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Hi all,

I solved this question by first combining Hot and Cold as they’re both running together. Why are we adding the rates? could someone help

Posted from my mobile device

\(\frac{1}{400} + \frac{1}{480} - \frac{1}{800}\)
\(=\frac{11}{2400} - \frac{1}{800}\)
\(=\frac{1}{300}\)
So the bath tub will take = 300s to fill up
300s = 5 min

Answer: D

Inputs= hot water + cold water

So;
hot water per minute= 1/8

Cold water per minute= 3/20

Rate of draining per minute= 3/40

Then;
Remaining water in the tank✓
= 1/8 + 3/20 - 3/40
=1/5 full
If 1min= 1/5full
Then, to be fully filled;
= 1min * 5/1
= 5mins

The correct answer is D.



Posted from my mobile device

I Think using efficiency method is fastest for these problems.

Hot water Cold Water Drain Plug
20/3 min 8 min 40/3 min

Lets assume tank capacity 120 ( multiple of LCM of all the times)

Efficiency of Taps:

Hot Water Cold Water Drain Plug
120/(20/3) 120/8 120/(40/3)
= 18 =15 =9

So total combined efficiency when att the taps and plugs are open = 8+15-9=24

So time required= 120/24= 5 hour.

Fastest solution when numbers are complicated...

Bunuel

Could you please guide me on how to quickly find the common factor? here i.e 4800. I generally use the LCM. It is kind of took me 3 minutes to solve this question.