Isolate the quantities you need to know and the ones you already do. For example, take this basic algebra problem: "If Mike can paint one room in three hours, and Bill can paint two rooms in four hours, then how long will it take Mike and Bill together to paint one room?" The quantities in this example are Mike's ratio of one room in three hours, and Bill's ratio of two rooms in four hours. The quantity you want to find is the sum of Mike's ratio with Bill's; that quantity can be used to get the answer.
Write your quantities down. Think about the kind of quantities you have: are they ratios? Sets of numbers? Lengths of time? In this case, you're dealing with lengths of time expressed as ratios. The best way to represent a ratio is with a fraction, so write the ratios as 1/3 and 2/4.
Use your formalized information to find the answer. Remember that in Step 1 you saw that the answer to the problem was the sum of the two ratios. So, add your two ratios. 2/4 = 1/2, so find 1/3 + 1/2. The lowest common multiple of 3 and 2 is 6, so multiply 1/3 by 2/2 and multiply 1/2 by 3/3. 2/6 + 3/6 = 5/6. You are not done yet, though; this quantity simply shows that Mike and Bill can paint five rooms in six hours.
Find the answer by re-reading the original applied problem. Notice the kind of answer that the problem asks for: How long does it take Mike and Bill to paint one room together? Right now you have the ratio, 5/6: read it as "5 rooms per 6 hours." What you need is a ratio with a 1 in the denominator, representing 1 room. So, write the equation as 5/6 = 1/x. You are using x to represent the answer itself.
Solve for x to find your answer. Multiply both sides by 6 to get 5 = 6/x. Multiply by x to get 5x = 6. Divide by 5 to get x = 6/5. Use your calculator to find 6/5 = 1.2. x = 1.2. So, it takes Mike and Bill 1.2 hours, or 1 hour and 12 minutes. You were able to find the answer because you could formalize it as a variable.