A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 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?
anonymous
 5 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?

This Question is Closed

JamesJ
 5 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 \(1/R\).

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

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

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

JamesJ
 5 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
 5 years ago
Best ResponseYou've already chosen the best response.4put it in your calculator if you like.

JamesJ
 5 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
 5 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.

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

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.4R = 0.0125 and hence 1/R = 80 hours, yes.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.