A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

pure water is poured at the rate of 3 gal/min to a tank containing 300 lbs. of salt dissolved in 100 gals. of water and solution kept while stirring, forced out at 2 gals/min. Find the amount of salt at the end of 1 hr. and 30 minutes?

  • This Question is Closed
  1. dumbcow
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Tank loses 2 gal/min while adding 3 gal/min for a net of 1 gal/min \[Volume = 100 + t\] Salt content in the tank starts at 300 and loses 2C lbs every min where C(t) is the concentration of salt at time t C(t) = Salt content/Volume \[C(t) = \frac{300-2t*C(t)}{100+t}\] solving for C(t) \[\rightarrow C(t) = \frac{300}{100+3t}\] Let S(t) be salt content at time t S(t) = C(t)*Volume \[\rightarrow \ s(t) = \frac{300(100+t)}{100+3t}\] when t=90 \[s(90) = \frac{300(190)}{100+270} = 203.57\]

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks for the effort dumb cow, but i already got the answer. . it's 83.10 lbs.

  3. dumbcow
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you please explain to me how you got that answer? Thanks

  4. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this problem is actually related to mixture problem related to differential equation application. . have you encountered this one?

  5. dumbcow
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no

  6. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    here, let me show you how i got it. .

  7. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1328684363825:dw| we got 100 +t as denominator for the because the rate of going in minus the rate in going out (3t - 2t) resulted to t. .

  8. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    to make the equation--\[dQ/dt=3(0) - 2(Q/100+t)\] we're finding the change of concentration

  9. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1328684946025:dw||dw:1328685032254:dw| cancel ln.|dw:1328685126662:dw| this is now our equation. .

  10. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now let's find the value for C or constant, given the initial number of salt (Q) which is 300 at t=0 |dw:1328685267814:dw| now that we have the value for constant, we can now find the remaining salt in lbs at t=90 mins.

  11. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1328685463206:dw|

  12. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that's how i got the answer. . kindly check if there are irregularities.

  13. dumbcow
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No it looks fine, thanks for the explanation. i didn't see where i could solve dQ/dt explicitly like that

  14. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    aah, yea me either got difficulties in solving the problem. but anyways, thanks for the medal.

  15. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.