Now the inflow of brine brings salt into the tank at the rate of 5 kg per minute
(as 25 × 200 g = 5 kg) and the outflow of brine takes salt out of the tank at the rate of
25 1000
40
y
y


 =
 kg per minute (as at time t, the salt in the tank is 1000
y
kg) Thus, the rate of change of salt with respect to t is given by
dy
dt  = 5
−y40
(Why )
or
1
40
dy
y
dt +
 = 5 (1)
Rationalised 2023-24
206
MATHEMATICS
This gives a mathematical model for the given problem