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If Samson is filling a bathtub with COLD water, it will take

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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

M04-37

Wanted to understand the way the numbers 12, 10 and 6 are arrived at in the net speed calculation.
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abhi758 wrote:
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

Wanted to understand the way the numbers 12, 10 and 6 are arrived at in the net speed calculation.


Times:
\(c=6\frac{2}{3}=\frac{20}{3}\);
\(h=8\);
\(d=13\frac{1}{3}=\frac{40}{3}\).

Remember that we can sum the rates. As rate is the reciprocal of time:
\(\frac{1}{c}+\frac{1}{h}-\frac{1}{d}=\frac{3}{20}+\frac{1}{8}-\frac{3}{40}=\frac{1}{5}=\frac{1}{t}\) --> \(\frac{1}{5}=\frac{1}{t}\) --> \(t=5\).

Answer: D.
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New post 08 Apr 2010, 04:14
Bunnel, Thanks for the prompt explanation!

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New post 09 Apr 2010, 23:16
Did same same Bunuel ...calculated the net gain per minute ...5 min.

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New post 06 Feb 2011, 15:03
Bunuel, please can you explain the concept behind summing the rate. if you could also point me to more questions like these on the forum ..it would be really helpful. Thanks.
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New post 06 Feb 2011, 15:27
ajit257 wrote:
Bunuel, please can you explain the concept behind summing the rate. if you could also point me to more questions like these on the forum ..it would be really helpful. Thanks.


This is very simple concept. For example if printer A can print 3 pages per hour and printer B can print 2 pages per hour then working simultaneously they can print 2+3=5 pages per hour.

Check this: word-translations-rates-work-104208.html#p812628

PS work problems: search.php?search_id=tag&tag_id=66
DS work problems: search.php?search_id=tag&tag_id=46
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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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New post 29 Dec 2014, 10:55
Hi Bunuel,

Why can't we directly add the times, as we need to calculate time only at the end

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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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Hi All,

While the approach would be slightly longer, you could use the Work Formula and some rate-based calculations to answer this question.

Work Formula = (A)(B)/(A+B)

We're told the two rates to "fill" the tub:

A = 6 mins 40 secs = 6 2/3 mins = 20/3 mins
B = 8 mins

(20/3)(8)/(20/3 + 8) = (160/3)/(44/3) = 160/44 mins to fill the tub

160/44 = 40/11 mins to fill the tub.

In 1 minute, 11/40 of the tub will be filled

We're also told how long it takes to drain the tub:

Drain = 13 mins 20 secs = 13 1/3 mins = 40/3 mins to drain the tub

In 1 minute, 3/40 of the tub will be drained

Now that we have the rates of the water going "in" and the water coming "out", we can combined them:

11/40 - 3/40 = 8/40 = 1/5

The "net effect" is that 1/5 of the tub is filled every minute.

For a full tub, we need (1/5)(5 minutes).

Final Answer:
[Reveal] Spoiler:
D


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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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New post 08 Sep 2017, 10:35
I understood the logic but I converted time into sec and then into mins at the last steps but I'm not getting ans as 5.can anyone solve for me with detail steps in seconds please?

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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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New post 08 Sep 2017, 14:44
Hi r19,

Can you list out your 'steps' and the work that you did? It might be that you knew how to answer the question, but you made a little math mistake (and that would be easier for another member to explain).

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If Samson is filling a bathtub with COLD water, it will take [#permalink]

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New post 09 Sep 2017, 06:12
rich ,
Sorry, I should have posted before
cold water = 6 mins 40 sec = 6*60=360+40 = 400 secs
hot water = 8 mins = 8*60 = 480 secs
drain = 13 mins 20 secs = 13*8=780+20=800 secs

equation
1/400+1/480-1/800
taking 10 out
1/40+1/48-1/80
taking 4 out
1/10+1/12-1/20
taking 2 out
1/5+1/6-1/10
lcm = 30
(6+5-1)/30 = 8/30
tell me where I made mistake

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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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New post 10 Sep 2017, 20:26
Bunuel wrote:
abhi758 wrote:
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

Wanted to understand the way the numbers 12, 10 and 6 are arrived at in the net speed calculation.


Times:
\(c=6\frac{2}{3}=\frac{20}{3}\);
\(h=8\);
\(d=13\frac{1}{3}=\frac{40}{3}\).

Remember that we can sum the rates. As rate is the reciprocal of time:
\(\frac{1}{c}+\frac{1}{h}-\frac{1}{d}=\frac{3}{20}+\frac{1}{8}-\frac{3}{40}=\frac{1}{5}=\frac{1}{t}\) --> \(\frac{1}{5}=\frac{1}{t}\) --> \(t=5\).

Answer: D.


Since there are 2 reverse operations fill and drain going on, we need to find the net fill - drain in 1 min .

In 1 min 3/20 of cold water is filled and 1/8 of hot water.

So net fill = 3/20+1/8 =11/40;

Water drained in a min = 3/40.

So in a min when 3 operations are simultaneous, it will fill 11/40-3/40 of water tub.
ie 1/5 of tub in 1 min. So the tub will be fully filled in 5mins.

Ans:D

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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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Hi r19,

From a math standpoint, you cannot "reduce" the fractions the way you did without changing their values. Here's a simple example:

1/10 + 1/20 = 2/20 + 1/20 = 3/20

However, if you "take 2 out" the way you did, then you would then end up with:

1/5 + 1/10 = 2/10 + 1/10 = 3/10

This is NOT the same end result (it's actually DOUBLE what it should be).

Your initial 'step' was to convert information into what occurs each second:

1/400 + 1/480 are the two "intakes" and the - 1/800 is the "outtake." Adding those fractions up, we get...

12/4800 + 10/4800 - 6/4800 = 16/4800 = 1/300

This means that with each second that goes by, 1/300 of the bathtub is filled. Thus, it takes 300 seconds = 5 minutes to fill the tub.

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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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New post 12 Sep 2017, 11:01
@rich....thank you..goot my mistake

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Re: If Samson is filling a bathtub with COLD water, it will take [#permalink]

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New post 17 Sep 2017, 17:13
So, let C be cold water and H, hot water. Thus, D stands for draining.

\(1/T = 1/C + 1/H - 1/D\)

Converting times:
C -> 6 minutes and 40 seconds are 400 seconds.
H -> 8 minutes are 480 seconds.
D -> 13 minutes and 20 seconds are 800 seconds.

So:

\(1/T = 1/400 + 1/480 - 1/800\)

\(1/T = (12+10-6)/4800\)

\(1/T = 16/4800\)

So, T = 4800/16 -> 300 seconds, or 5 minutes.

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Re: If Samson is filling a bathtub with COLD water, it will take   [#permalink] 17 Sep 2017, 17:13
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