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

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08 Apr 2010, 01:31

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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.

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.

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

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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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.

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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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?

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).

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

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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

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

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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.

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.

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