Problem Solving In Algebra With Solution

Problem Solving In Algebra With Solution-79
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 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.

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.

Think of the calculator as merely a tool that makes the journey easier.

After all, you wouldn’t want a surgeon to crack your ribs and perform a heart transplant without first identifying the source of your chest pains. Now that you understand the word problem’s purpose, determine the answer’s unit.

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.

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.

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.

On the other hand, if you write down each step while solving the problem, you can retrace your steps and make sure your answer is correct.

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.

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