Question

A water tank has 500 litres of water initially and water is pumped into the tank at the rate of 8 litres per minute. Write and expression to show the the amount of water in the tank after t hours

Answer 1

Answer:

s

A

11

Input rate = 10 gm/min

After time t volume of tank = 50 + (2-1)t

Concentration of salt in time t=

50+t

m

gm/lit

Output rate =

50+t

m

.1gm/min

⇒

dt

dm

=

50+t

−m

+10

⇒m(50+t)=∫10(50+t)dt

⇒m(50+t)=500t+5t

2

+c

⇒(∵att=0,m=0⇒c=0)

⇒m(50+t)=5(100t+t

2

)

⇒m=5t(

50+t

100+t

)gm