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viniterranova
 3 years ago
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?
viniterranova
 3 years ago
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?

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JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.4The 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 \(1/R\).

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

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

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

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

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

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

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.4For 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.

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

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

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