Question 1153922
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<pre>

Let x be the new speed, in km/h.

Then the regular speed is (x-500) km/h.


The regular flight time is  {{{3000/(x-500)}}} hours.

The new time flight is      {{{3000/x}}} hours.


The difference is one hour (1 hour), which gives you THIS "time equation"


    {{{3000/(x-500)}}} - {{{3000/x}}} = 1   hour.


To solve the equation, multiply both sides by  x*(x-500).  You will get


    3000x - 3000*(x-500) = x*(x-500)

    300*500 = x*(x-500)

    x^2 - 500x - 1500000 = 0

    {{{x[1,2]}}} = {{{(500 +- sqrt(500^2 +4*1*1500000))/2}}} = {{{(500 +- sqrt(6250000))/2}}} = {{{(500 +- 2500)/2}}}.


Only positive root makes sense  x = {{{(500 + 2500)/2}}} = 1500.


<U>ANSWER</U>.  The new speed is 1500 km/h.


<U>CHECK</U>.   The regular speed is then 500 km/h lover, i.e.  1000 km/h.


         Check the "time equation"  {{{3000/1000}}} - {{{3000/1500}}} = 3 - 2 = 1 hour.   ! Precisely correct !
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Solved.