basic algebra word problem, find the speed

Question

SOLVE IN TERMS OF TWO VARIABLES: A pilot flies a distance of 600 km. He could fly the same distance in 30 minutes less time by increasing his average speed by 40 km/hr. Find his actual average speed. Let x = actual average speed, _____= new average speed, _____= time to fly 600 km at actual average speed, _____= time to fly 600 km at new average speed, _____= difference in time using the two speeds,equation:_________________=____________

Answer 1

time1=distans/speed=600 km/speed1 . . . time1 -30 minuts=600 / (speed1+40) . . . (time1 -0.5 ours)=600 / (speed1+40) . . . (speed1+40)*(time1-0.5 ours)=600 . . . speed1*time1 +40*time1 -0.5speed1 -0.5*40=600 . . . but speed1*time1=600 . . . so, 40*time1 -0.5speed1-20=0 . . . but speed1=600/time1 . . . so, 40*time1 -0.5*(600/time1)-20=0 . . . or 40*time1^2 -20*time1 -300=0 . . . or 4*time1^2 -2*time1 -30=0 . . . quadratik equashun giv time1=3 or -2.5, so time= 3 ours . . . 600 km/3 ours...speed=200 k/our . . . time2=time1-0.5=2.5 ours . . . speed2=600/2.5=240 k/our