Question 1131120
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Julio intends to drive his motorbike to a friend's house 200 kilometers away. If he increases his planned rate {{{highlight(cross(of_speed))}}} 
by 10km/hr, he can decrease his travel time by 40 minutes. What is his planned rate ?  {{{highlight(cross(of speed))}}}
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            (!)  NEVER  say  "rate of speed"  (!)  


            THERE  IS  NO  such a term.    It  DOES  NOT  EXIST  and is  NEVER  USED  (!)


            As soon as you use it,  you demonstrate that you are not familiar with the correct usage of the terms in the subject  !



<pre>
Let x be the planned rate in kilometers per hour. 


The the hypothetical speed is (x+10) kilometer per hour


The planned time is  {{{200/x}}} hours.


The hypothetical time is  {{{200/(x+10)}}}  hours.


The difference is  40 minutes, which is  {{{2/3}}} of an hour.


It gives you an equation


    {{{200/x}}} - {{{200/(x+10)}}} = {{{2/3}}}.


It is your basic equation, and when you got it, you completed the setup.


To solve the equation, multiply its both sides by 3*x*(x+10). You will get


    600*(x+10) - 600x = 2x*(x+10),

    600x + 6000 - 600x = 2x^2 + 20x

    2x^2 + 20x - 6000 = 0

    x^2 + 10x - 3000 = 0

    (x+60)*(x-50) = 0.


Only positive root x= 50 is meaningful.


The answer is: the planned speed is  50 kilometers per hour.
</pre>

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