Algebra-2

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

 

Step 1: Determine the work rate of Cleaner 1

If Cleaner 1 can finish cleaning the room in  hours, then the work rate of Cleaner 1, denoted as , is  (i.e., the fraction of the room that Cleaner 1 can clean in one hour).

 

Step 2: Determine the combined work rate of the two cleaners

When both cleaners work together, they can finish the room in  hours. So the combined work rate of the two cleaners, denoted as , is  (the fraction of the room that they can clean together in one hour).

 

Step 3: Calculate the work rate of Cleaner 2

Let the work rate of Cleaner 2 be . Since the combined work rate of the two cleaners is equal to the sum of their individual work rates, we have the equation:

 

Substituting the known values of  and

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