Samson can fill an empty bathtub with a cold water tap in 6 minutes

Question

Samson can fill an empty bathtub with a cold water tap in 6 minutes and 40 seconds or with a hot water tap in 8 minutes. Draining the full bathtub, while the plug is out, takes 13 minutes and 20 seconds. How long will it take Samson to fill the empty bathtub completely with both the cold and hot taps running, while the plug is out?

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

M04-37

Bunuel · Accepted Answer

Samson can fill an empty bathtub with a cold water tap in 6 minutes and 40 seconds or with a hot water tap in 8 minutes. Draining the full bathtub, while the plug is out, takes 13 minutes and 20 seconds. How long will it take Samson to fill the empty bathtub completely with both the cold and hot taps running, while the plug is out?

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

The cold water tap can fill the bathtub in  6\frac{2}{3}=\frac{20}{3}  minutes, giving a rate of  \frac{3}{20}  tubs per minute. Similarly, the hot water tap can fill the bathtub in 8 minutes, giving a rate of  \frac{1}{8}  tubs per minute. On the other hand, draining the bathtub takes  13\frac{1}{3}=\frac{40}{3}  minutes, giving a rate of  \frac{3}{40}  tubs per minute.
 
Therefore, the net inflow rate when both the cold and hot water taps are running and the drain is open is given by  \frac{3}{20} + \frac{1}{8}-\frac{3}{40}=\frac{6}{40} + \frac{5}{40}-\frac{3}{40}=\frac{8}{40}=\frac{1}{5}  tubs per minute.
 
Since the rate is the reciprocal of time, the time it will take to fill the bathtub completely is therefore 5 minutes.

Answer: D

abhi758 · Answer

Bunnel, Thanks for the prompt explanation!

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made,
Rich

r19 · Answer

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?

EMPOWERgmatRichC · Answer

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).

GMAT assassins aren't born, they're made,
Rich

Arsh4MBA · Answer

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

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

Confusion · Answer

Easier method
Rates are 6and 2/3, 8 mins and 13 and 1/3
fraction is 20/3, 8, 40/3
In 1 min fill rates are 3/20, 1/8, -3/40
Let capacity be 80 liter
So filled in 1 min is 12, + 10 - 6 = 16
Therefore time taken is 80 liter/16 liter = 5 min

Samson can fill an empty bathtub with a cold water tap in 6 minutes

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Samson can fill an empty bathtub with a cold water tap in 6 minutes

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