Question

Water flows into a pond at a rate of 300√ t gallons per hour and flows out at a rate of 400 gallons per hour. After one hour, there are 10,000 gallons of water in the pond. How much water is in the pond after 9 hours?

Answer 1

this is algebra problem right? not calculus?

Answer 2

This is a calculus problem

Answer 3

I'm having a hard time setting up the equation

Answer 4

ohh related rates? i dont like calculus sorry hahaha =)))

Answer 5

its alright :)

Answer 6

Let's see. We have an inflow rate \(f'(x)=300t^{\frac{1}{2}}\) and an outflow rate \(g'(x)=400\). At any given point of time, \(f(x)=200t^{\frac{3}{2}}+C,g(x)=400t+C, f(x)-g(x)+c\) so we can say \(\left[200t^{\frac{3}{2}}-400t+C=10000\right]_{t=1}\) gives us the amount of water at any given time.

Answer 7

From here it should be a matter of solving, and plugging in.

Answer 8

Thank you :)
trying to figure out the equation always gets me stuck.

Answer 9

Problem visualization is almost always the hardest part. It requires personal input. In my opinion, of course.

Answer 10

Well I guess it's the matter of practice practice practice :)