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When you’re solving an algebra problem in your head, you won’t have any way to go back and walk through your solution again if you missed a step.
Many of these problems are not terribly realistic — since when can two laser printers work together on printing one report?
— but it's the technique that they want you to learn, not the applicability to "real life".
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.
If you're not sure how you'd do this, then think about it in terms of nicer numbers: If someone goes twice as fast as you, then you take twice as long as he does; if he goes three times as fast as you, then you take three times as long as him.
Solving Algebra word problems is useful in helping you to solve earthly problems.
While the 5 steps of Algebra problem solving are listed below, this article will focus on the first step, Identify the problem.When you underline or highlight these important parts, you can quickly reference the things you need to without having to read through the entire problem again.This makes it easier to go back and double check that you’ve got the right equations and variables set up, without losing your train of thought halfway through solving the algebra word problem.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.In this case, I know the "together" time, but not the individual times.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 example, will the answer be in miles, feet, ounces, pesos, dollars, the number of trees, or a number of televisions?When you’re solving algebra word problems, it’s smart to have a plan of attack ready to follow.When you read through the entire problem, you’ll have a better chance of noticing any variables that are given and any that you need to solve for.These keywords can go a long way in helping you determine how to set up the algebra equations.