Question 1143190
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<pre>
Let x = his rate on the trip from his home, in miles per hour (which is the unknown value under the question).


Then his rate on the way back is (x+30) mph.


The time spent for the trip "to there" is  {{{40/x}}}  hours.


The time spent for the trip back is  {{{40/(x+30)}}}  hours.


The total time is 2 hours, which gives you this "time" equation


    {{{40/x}}} + {{{40/(x+30)}}} = 2   hours.


To solve it, multiply both sides by  x*(x+30). You will get


    40*(x+30) + 40x = 2x*(x+30),

    40x + 1200 + 40x = 2x^2 + 60x

    2x^2 - 20x - 1200 = 0

    x^2  - 10x - 600  = 0

    (x-30)*(x+20) = 0


There are two roots,  x= 30  and x= -20,  but only positive  x= 30 makes sense.


<U>ANSWER</U>.  His rate "to there" is  30 mph.


<U>CHECK</U>.  {{{40/30}}} + {{{40/(30 + 30)}}} = {{{40/30}}} + {{{40/60}}} = {{{1}}}{{{1/3}}} + {{{2/3}}} = 2 hours.    ! 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 and economic. &nbsp;Going in this way, &nbsp;you will not 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/Earthquake-waves.lesson>Earthquake waves</A> 

&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.