A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. 50t+ 1²+ c Q' (t) = X Check your variables you might be using an incorrect one. 50+t (b) Find the quantity of salt in the tank as it's about to overflow. 38.5 X
A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. 50t+ 1²+ c Q' (t) = X Check your variables you might be using an incorrect one. 50+t (b) Find the quantity of salt in the tank as it's about to overflow. 38.5 X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5
pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5
gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min).
(a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows.
50t+
Q' (t) =
X Check your variables you might be using an incorrect one.
50+t
(b) Find the quantity of salt in the tank as it's about to overflow.
38.5
X
Oll
✓
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W
#
3
e
t² + c
C
$
4
%
5
+
6
&
7
O
*
8
O
9
11
OF
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