Let yt denote the quantity of salt in the tank at time t Wha

Solution

Let y(t) be g/L of salt in tank at any time t salt initially present = (500*10) = 5000 gm now net rate of accumulation of water in tank = (inflow rate) - (outflow rate) = 20L/min salt coming in = (80 L/min)*(60 g/L) = 4800 g/min the tank has 500L in vacant space, so time taken to fill this = 500/20 = 25 min after time 25 min, tank just overflows then if we balance the salt, salt in tank = (salt initially present) + (salt due to inflow) - (salt lost due to outflow) salt in tank = 1000*y grams .. (as the volume of tank when is just overflows is 1000 L and y is g/L of salt that is present at time t) salt initially present = 5000 gms salt due to inflow = (4800*25) = 120,000 gms salt lost due to outflow = (60*y*25) = 1500y....( 60L/min is out flow rate, so at t = 25 min and salt conc y g/L, salt is lost at rate of (60L/min)*(25 min)*(y g/L) ) so balance 1000y = 5000 + 120,000 - 1500y hence, y = 50 g/L so grams of salt present in tank when it just overflows = (1000*y) = 50,000 gms