Water is being pumped continuously into a tank at a rate that is inversely proportional to the amount of water in the tank;that is, ,where y is the number of gallons of water in the tank after t minutes .Initially there were 5 gallons of water in the tank,and after 3 inutes there were 8 gallons.How many gallons of water were in the tank at time 20 minutes?
A)
B)
C)

Question

​Water is being pumped continuously into a tank at a rate that is inversely proportional to the amount of water in the tank;that is,  ,where y is the number of gallons of water in the tank after t minutes  .Initially there were 5 gallons of water in the tank,and after 3 inutes there were 8 gallons.How many gallons of water were in the tank at time 20 minutes? ​
A)​ 
B)​ 
C)​

Quizplus · Accepted Answer

We are given that the rate of water pumped into the tank is inversely proportional to the amount of water in the tank. Let's first find the constant of proportionality, k. We know that when t=0, y=5. Substituting these values in the given equation, we get:

5k = 1
k = 1/5

So, the equation that models the amount of water in the tank is:

y = 5 + (1/5)t

We are asked to find the amount of water in the tank at t=20. Substituting t=20 in the above equation, we get:

y = 5 + (1/5)(20) = 9

Therefore, the answer is C, 9 gallons.

​Water Is Being Pumped Continuously into a Tank at a Rate

Water Is Being Pumped Continuously into a Tank at a Rate