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.
Above anything else, algebra word problems need practice on a consistent basis.
By working a few algebra word problems each day, you’ll be able to fine-tune your solving methods and work on any of the rough parts.
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.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".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.Having a written record of each variable also helps when it comes time to give your solution, as you know what variable has the answer in it!Writing down notes also functions as a way to double-check when you’ve got your solution ready.Solving word problems may seem difficult, but when you read through the problem and can figure out what the specific equation is, it’s no harder than a regular algebra problem.Here are some tips for getting a solid system of steps to follow when you are solving algebra word problems: While it might seem tempting to start working on the problem as soon as you get halfway through the first sentence, you need to be patient.This way, you won’t have to try to remember what each variable is that you’re solving for, or whether you’re multiplying or dividing by two in the next equation.You can concentrate on each small task within the algebra problem, and then put the pieces together at the end.