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 Amsco Integrated Algebra I: Using Systems of Equations to Solve Verbal Problems
This is a free lesson from our course in Amsco's Integrated Algebra
In this lesson you’ll learn how to solve verbal problems by using systems of equations. You may recall previous learning to solve word problems by using one variable. However, in real life these problems can be more complex calling to solving systems of equations more easily by using two variables. Solving systems of equations can use various methods like - substitution, elimination using addition and subtraction, and elimination using multiplication etc. The approach will be to read the problem carefully, analyze and solve. (More text below video...)
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(Continued from above) For example: Given- A passenger jet took three hours to fly 1575 miles in the direction of the jet stream. The return trip against the jet stream took 3.5 hours. What was the jet's speed in still air and the jet stream’s speed? The solution is as below:
You need to know first that ‘in still air’ (for plane) or ‘in still water’" (for boat), mean the speedometer reading of each respectively. Now pick the variables and proceed – say use j for ‘the plane's speedometer reading’ and w for ‘the wind speed’.
• in both the cases, total distance traveled equals to the combined speed multiplied by time taken i.e.
• with the jet stream:   (j+ w)(3) = 1575
against the jet stream:  (j– w)(3.5) = 1575
• divide the first and second equation by 3 and 3.5 respectively.
• then the equations are j+ w = 525
                                  j– w = 450
• adding these equations results in 2j= 975 i.e. j= 487.5, and w must then be 37.5.
The jet's speed was 487.5 mph in still air and in other case the speed was 37.5 mph, as the final answer.
The video above explains; more details on Using Systems of Equations to Solve Verbal Problems, with the help of several examples and their solutions.

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