Question

A large mixing tank currently contains 225 225 gallons of water, into which 5 5 pounds of sugar have been mixed. A tap will open, pouring 20 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 4 4 pounds per minute. Find the concentration (pounder per gallon) of sugar in the tank after t t minutes.

Answer 1

Answer: Hello mate!

you put every number twice, I will consider that in this problem we have:

225 gallons of water initial with 5 pounds of sugar. then each minute you add 20 gallons of water and 4 pounds of sugar.

the concentration is defined as pounds of sugar divided by the gallons of water. The gallons of water are 225 initially and 20 per minute, this is written as 225 + 20tt, where t is the minutes. The pounds of sugar is 5 + 4 per minute, then this can be written as 5 + 4t

$C(t) = \frac{5 + 4t}{225 + 20t}$

this is the equation that describes the concentration in pounder per gallon after t minutes.