Question

An empty tank has a capacity of 54 liters. it is being filled at the rate of dy/dt= 3 square root t. where y is the amount of water in the tank in liters and t is time in seconds. after how many seconds will the tank be full

Answer 1

To answer this question, let us start by making a representation of the situation

We are asked to calculate in how much time the tank will be filled, note that 3 liters of water are falling into the tank every second so we have the next sequence of states

* After one second, there are 3 liters in the tank;

*After two seconds, there are 6 liters in the tank;

* After 3 seconds, there are 9 liters on the tank

And so on, so to find how many seconds it will take to fill the tank we must find haw many times i can put 3 liters of water in the tank, that is, we have to calculate:

$How\text{ many times I can put 3 liters in the tank= }\frac{54}{3}=18=\text{ It takes 18 seconds }$

We conclude that to fill a tank with capacity 54 liters putting water at rate of 3 liters per second it will take 18 seconds.