SOLUTION: How do I express a rational function that describes the following situation? A large mixing tank currently contains 200 gallons of water, into which 10 pounds of sugar have been

Question 1137047: How do I express a rational function that describes the following situation?
A large mixing tank currently contains 200 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pouring 10 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 3 pounds per minute. How do I find the concentration (pounds per gallon) of sugar in the tank afer t minutes?
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Let be the number of minutes since the tap opened.
given:mixing tank currently contains gallons of water
since the water increases at gallons per minute, and the sugar increases at pound per minute, these are constant rates of change.
this tells us the amount of water in the tank is changing linearly, as is the amount of sugar in the tank. We can write an equation independently for each:
water: in gallons
sugar: in pounds
The concentration, , will be the ratio of pounds of sugar to gallons of water:

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let t equal the number of minutes that have transpired.

the water starts off at 200 gallons and receives 10 additional gallons per minute.

the sugar starts of at 10 pounds and receives 3 additional pounds per minute.

the formula for the water is 200 + 10 * t.

the formula for the sugar is 10 + 3 * t.

the ratio of sugar to water is (10 + 3 * t) / (200 + 10 * t).

that's your concentration.

it's in the form of a ratio.

multiply the ratio by 100 and you get the concentration as a percent.

every additional minute, 3 pounds of sugar are added and 10 gallons of water are added.

at t = 0, the ratio of sugar to water is 10 / 200 = .05 which is a concentration of 5%.

at t = 1, the ratio of sugar to water is (10 + 1 * 3) / (200 + 1 * 10) = 13 / 210 = .0619047619 which is a concentration of about 6.2%.

at t = 5, the ratio of sugar to water is (10 + 5 * 3) / (200 + 5 * 10) = 25 / 250 = .1 which is a concentration of 10%.

etc.....

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