Bunuel wrote:
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
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 3CW=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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