Solve algebra equation with missing values.

This book teaches how to set up a math problem, not how to do the math. I need help with the math on the last page next to the red arrow. v=x/t. The missing values in this physics problem are circled. If x and t are missing, how is it possible to get v? It is my understanding that I choose the equation that has only one missing value, rearrange the equation and solve for that missing value. But in this case there are too  many missing values.

Thanks.
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kadinAsked:
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aburrConnect With a Mentor Commented:
The v for the truck is given at the start.
do what is asked and solve for xT, that is xT = vT * t
do not worry that you do not have a value yet for t. That comes at the bottom. That is the beauty of using symbols instead of numbers. You do not need the numbers until the last step
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aburrCommented:
But there is not just one relevant equation
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kadinAuthor Commented:
I need help with the steps taken on this final page. Step one is solve for x in symbols next to red arrow. This is where I get hung up. What exactly did the author do to resolve some of the first missing values  that are circled? Thanks.
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kadinAuthor Commented:
There are five equations on the right to choose from. Each of these equations has at leased two missing values. I thought it wasn't possible to get an answer if there is more than one missing value in the equation. So how do I begin to solve it?
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aburrCommented:
xC = xT + 20 is the co9nnecting equation.
xC is given by the equation  just below the Car
NOW you have an equation where everything is known except t. solve for t and put it in your previous equations as needed.
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kadinAuthor Commented:
That is the beauty of using symbols instead of numbers. You do not need the numbers until the last step

Ok. I am learning something here. So then my real challenge is understanding the purpose of the quadratic formula. Is that right? That is a magical area I don't fully understand. It can be used to derive the first unknown value, in this case T.
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aburrCommented:
"I thought it wasn't possible to get an answer if there is more than one missing value in the equation"
That is true when you have only one equation but when you have two equation you can usually solve for two unknowns.
You have five equations so it is easy to solve for two unknowns
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aburrConnect With a Mentor Commented:
The quadratic comes from the simple equation just above it
xC = xT + 20
xC from the right under Car
xT as you have gotten at the red arrow.
Everything in there except t is known (remember that vC = 0)
solve for t
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kadinAuthor Commented:
I may have five equations, but each equation has two unknowns. This part confuses me. How do I solve an equation with two unknowns. I guess your saying I can some how mix the equations to remove the unknowns until I have an equation with just one unknown.
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kadinAuthor Commented:
Thanks for your help on this. I am running out of time for today. I will think about what you said and study this some more. Tomorrow maybe I post another question.
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aburrCommented:
suppose you have two equations in two unknows.
You solve the first for one unknown (put it on the left hand side) thus there is only one unknown on the right hand side
Now in the second equation you replace every occurrence of the left hand side with the right hand side. Thus the second equation has only one unknown. Solve. Put the result into the first equation and you have now found two unknowns with the two equations.
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