Question 1150378
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<pre>

Let "x" be the rate on the way to the game.


Then you have this "time" equation


    {{{102/(x-17)}}} - {{{102/x}}} = 1 


saying that the difference in times going and back is 1 hour.


Multiply both sides by x*(x-17).


    102x - 102*(x-17) = x*(x-17

    102*17 = x^2 - 17x

     x^2 - 17x - 1734 = 0

    {{{x[1,2]}}} = {{{(17 +- sqrt(17^2 + 4*1734))/2}}} = {{{(17 +- 85)/2}}}.


Only positive root makes sense  x = {{{(17+85)/2}}} = 51.


<U>ANSWER</U>.  The rate on the way to the soccer game was  51 mph.


<U>CHECK</U>.   {{{102/(51-17)}}} + {{{102/51}}} = {{{102/34}}} - {{{102/51}}} = 3 - 2 = 1 hour.   ! Correct !
</pre>

Solved.


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Using &nbsp;"time" &nbsp;equation is the &nbsp;STANDARD &nbsp;method of solving such problems.


It is simple, &nbsp;logical, &nbsp;straightforward, &nbsp;economic and robust &nbsp;(work in standard way for any input data). 


Going in this way, &nbsp;you will never make a mistake - the logic of the method 
prevents you of making mistakes.


From this lesson, &nbsp;learn on how to write, &nbsp;how to use and how to solve a &nbsp;"time" &nbsp;equation.


To see many other similar solved problems, &nbsp;look into the lessons

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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Time-equation-HOW-TO-write-it-and-how-to-solve-it.lesson>Time equation: HOW TO use, HOW TO write and HOW TO solve it</A> 

in this site.