One of the pipes' times is expressed in terms of the other pipe's time, so I'll pick a variable to stand for one of these times. Since the faster pipe's time to completion is defined in terms of the second pipe's time, I'll pick a variable for the slower pipe's time, and then use this to create an expression for the faster pipe's time: Then I make the necessary assumption that the pipes' contributions are additive (which is reasonable, in this case), add the two pipes' contributions, and set this equal to the combined per-hour rate: Note: I could have picked a variable for the faster pipe, and then defined the time for the slower pipe in terms of this variable.
The method of solution for "work" problems is not obvious, so don't feel bad if you're totally lost at the moment.
There is a "trick" to doing work problems: you have to think of the problem in terms of how much each person / machine / whatever does Since the unit for completion was "hours", I converted each time to an hourly rate; that is, I restated everything in terms of how much of the entire task could be completed per hour.
For these problems, you are often asked to interpret what a variable or a constant means in the situation described, or you might be asked what kinds of conclusions can be drawn from a survey.
These types of problems often have no “math” involved, and instead ask you to think logically about a situation.
To do this, I simply inverted each value for "hours to complete job": My first step is to list the times taken by each pipe to fill the pool, and how long the two pipes take together.
Solving Word Problems In Math
In this case, I know the "together" time, but not the individual times.
Being able to identify problems by type on the SAT is a useful prep exercise and can help you on the day you take the test.
You may want to use the Math section from a free practice SAT test and circle all of the word problems.
Then, read each word problem and assign it to one of the types.
Doing this will help you see the commonalities between different types of questions and will allow you to spend less time on the actual test wondering what type of question you’re dealing with!