Algebra-2

The following is the analysis and solution steps for this problem:

 

Step 1: Calculate the filling rate of Pipe 1

The filling rate of Pipe 1 is defined as the portion of the tank it can fill per unit of time. If Pipe 1 can fill the tank in  hours, then the filling rate of Pipe 1, denoted as , is  (tank per hour).

 

Step 2: Calculate the combined filling rate of the two pipes

When both pipes are open,  the tank fills in  hours. So the combined filling rate of the two pipes, denoted as , is  (tank per hour).

 

Step 3: Calculate the filling rate of Pipe 2

Let the filling rate of Pipe 2 be . Since the combined filling rate of the two pipes is equal to the sum of their individual filling rates, we have:

 

We know that  and

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