Answer:
Step-by-step explanation:
If you assume concentration of salt per unit water remains constnat, find the constant.
Initially, for 400 gal of water, you have 20 pounds of salt
20lb/400gal=0.05lb salt per gal of water.
Now do part a)
I will use the following variables:
: lb of salt in tank at time t
: lb of salt pumped out at time t
: lb of salt pumped in at time t
: lb of salt initially in tank
the equation is
total salt=initial salt+salt in-salt out

we know that
is 20lb
is 5 gal per minute, but we want lbs salt so 5gal/min*0.05lb/gal=0.25lb/min. but this is per time, so multiply by t to get 0.25t
is 4gal per minute, but we want lbs salt so 3gal/min*0.05lb/gal=0.20lb/min. but this is per time, so multiply to get 0.20t
subsitute all in



part b)
to solve this initial value problem, I would need to be given either a goal amount of salt (
) or a time elapsed
. Since none are given, the IVP cannot be solved.