Algebra-2

The following is the step-by-step analysis to solve this problem:

 

Step 1: Calculate the rate of drainage of Pipe 1

Let the volume of the tank be . If Pipe 1 can drain the entire tank in  hours, then the rate of drainage of Pipe 1 (the amount of water it drains per hour), denoted as , is given by the formula  (volume divided by time).

 

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

When both pipes are open, the tank drains in  hours. So the combined rate of drainage of the two pipes, denoted as , is

 

Step 3: Calculate the rate of drainage of Pipe 2

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

 

Substituting  and  into the above equation, we get:

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