Question 88417
Two cars leave an intersection at the same time. One travels north and the other heads west traveling 10mph faster. After 1 hour, they are 50 miles apart. What were their speeds?
Let the speed of the car travelling towards north be = x m/hr
then the speed of the car travelling towards west    = (x+10)m/hr
  after 1 hr distance between them is given to be = 50 miles

  After 1 hr distance travelled by the car towards north = x.1 = x miles
   After 1 hr distance travelled by the car towards west = (x+10).1 = (x+10) mil
     therefore using pythagoras theorem we get (50)^2 = x^2+(x+10)^2
                                             2500 = x^2+x^2+20x+100
                                         2500-100 = 2x^2+20x
                                             2400 = 2x^2+20x 
                                        dividing by 2 throughout 
                           we get 1200 = x^2+10x
                                 x^2+10x-1200 = 0          
                               x^2+40x-30x-1200=0
                             x(x+40)-30(x+40) = 0
                               (x+40).(x-30) = 0  or x-30 = 0  or x = 30
  speed of the car towards north is = 30 miles/hr
  speed of the car towards west is  = 40 miles/hr