SOLUTION: Hi A plane took off 1 hour later for its destination 3000km away. In order to reach the destination on time the pilot increased speed by 500km per hour. What is the new sp

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

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


The regular flight time is   hours.

The new time flight is       hours.


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


     -  = 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

     =  =  = .


Only positive root makes sense  x =  = 1500.


ANSWER.  The new speed is 1500 km/h.


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


         Check the "time equation"   -  = 3 - 2 = 1 hour.   ! Precisely correct !