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viniterranova
Group Title
A tank has two taps that can fill it
within 24 hours and 30 hours respectively, and a drain that
empties in 16 hours. If we open simultaneously
the whole set (two faucets and a drain), how
time the tank will be filled?
 3 years ago
 3 years ago
viniterranova Group Title
A tank has two taps that can fill it within 24 hours and 30 hours respectively, and a drain that empties in 16 hours. If we open simultaneously the whole set (two faucets and a drain), how time the tank will be filled?
 3 years ago
 3 years ago

This Question is Closed

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
The way to think of this and all problems like this is in terms of rates. The first tap fills 1/24th of a tank per hour; the second tap at a rate of 1/30. Therefore their combined rate is \( 1/24 + 1/30 \). The drain drains the tank at a rate of 1/16. Therefore the combined rate of all three is \[ R = \frac{1}{24} + \frac{1}{30}  \frac{1}{16} \] Then the time required to fill the tank is \(1/R\).
 3 years ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
I have found 10,43 hours. Am i right?
 3 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
What value do you have for R? 10.43 hours isn't right.
 3 years ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
What is the right value?
 3 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
As R = 1/24 + 1/30  1/16, just do the math. What value do you get for R?
 3 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
put it in your calculator if you like.
 3 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
I get R = 0.0125 = 1/80 . Hence the number of hours 1/R = ...
 3 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
For the record, if there was no drain, then the two taps would fill the sink at a combined rate of 1/24 + 1/30 = 0.075 and therefore the sink would fill in 1/0.075 = 13.3 hours. Whatever answer you get with the drain, it had obviously better be longer than 13.3 hours.
 3 years ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
I get 0,1249 for R.
 3 years ago

viniterranova Group TitleBest ResponseYou've already chosen the best response.0
So the righ answer is 80 hours.
 3 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
R = 0.0125 and hence 1/R = 80 hours, yes.
 3 years ago
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