Problema Solution
a winery has a var with two pipes leading to it. The inlet pipe can fill the vat in 4 hours, while the outlet pipe can empty it in 7 hours. How long will it take to fill the vat if both pipes are left open?
Answer provided by our tutors
Let y(t) stand for the fraction of the vat filled at a time 't'. We can write:
y'=(1 vat/4hours)t-(1 vat/7hours)t
Therefore:
(dy)=((1/4)t-(1/7)t)dt
y(t)=(1/8)t^2-(1/14)t^2+c
We can solve for c, by using the initial conditions y(0)=0
c=0
Therefore:
y(t)=(1/8)t^2-(1/14)t^2
Now, we want to know t, when y(t)=1 (the vat is full)
1=(1/8)t^2-(1/14)t^2
Solving for t, we get:
t=4.32 hours