Algebra-2

Here's the step-by-step analysis for solving this problem:

 

Step 1: Determine the filling rate of Hose 1

Let's assume the volume of the swimming pool is . If Hose 1 can fill the pool in  hours, then the rate of filling of Hose 1 (the amount of the pool it fills per hour), denoted as , is given by .

 

Step 2: Determine the combined filling rate of the two hoses

When both hoses are used together, the pool fills in  hours. So the combined filling rate of the two hoses, denoted as , is .

 

Step 3: Determine the filling rate of Hose 2

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

 

Substituting  and  into the equation, we get:

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