A large tank contains 140 litres of water in which 20 grams of salt is dissolved. Brine containing 15 grams of salt per litre is pumped into the tank at a rate of 6 litres per minute. The well mixed solution is pumped out of the tank at a rate of 3 litres per minute. (a) Find an expression for the amount of water in the tank after t minutes. (b) Let x(t) be the amount of salt in the tank after t minutes. Which of the following is a differential equation for x(t)? (A) dx = 90 3 x(t) 140 + 3t = 90 − x(1) (F) / (I) = 6 dt 6.x(t) 140 + 3t (B) d 6 18 3 x(t) 140 + 6t 3 140 x(t) (G) 18 = 18 3 x(t) 140 + 6t 6 x(t) 140 + 6t (H) 90 140 x(t) 6.x(t) 140 + 3t
A large tank contains 140 litres of water in which 20 grams of salt is dissolved. Brine containing 15 grams of salt per litre is pumped into the tank at a rate of 6 litres per minute. The well mixed solution is pumped out of the tank at a rate of 3 litres per minute. (a) Find an expression for the amount of water in the tank after t minutes. (b) Let x(t) be the amount of salt in the tank after t minutes. Which of the following is a differential equation for x(t)? (A) dx = 90 3 x(t) 140 + 3t = 90 − x(1) (F) / (I) = 6 dt 6.x(t) 140 + 3t (B) d 6 18 3 x(t) 140 + 6t 3 140 x(t) (G) 18 = 18 3 x(t) 140 + 6t 6 x(t) 140 + 6t (H) 90 140 x(t) 6.x(t) 140 + 3t
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 large tank contains 140 litres of water in which 20 grams of salt is dissolved. Brine containing 15 grams of salt
per litre is pumped into the tank at a rate of 6 litres per minute. The well mixed solution is pumped out of the tank
at a rate of 3 litres per minute.
(a) Find an expression for the amount of water in the tank after t minutes.
(b) Let x(t) be the amount of salt in the tank after t minutes. Which of the following is a differential equation for
x(t)?
(A)
(E)
(I)
dt
90
||
3 x(t)
140 + 3t
6
(B) d
6 x(t)
140 + 3t
3 x(t)
140 + 6t
dt
dx
dx
3
= 90 − x(1) (F) = 18 - 1*(7) (G) = 18
-
dt
dt
140 x(t)
(C)
dx
dt
= 18
3 x(t)
140 + 6t
6 x(t)
140 + 6t
(D)
(H)
dx
= 90
3
140 x(t)
6 x(t)
140 + 3t
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Transcribed Image Text:Now suppose that
the tank has an open top
and has a total capacity of 242 litres. How much salt (in grams) will be in the tank at the instant that it begins to
overflow?
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