SOLUTION: A jet flew 1200 miles with a tailwind of 50 mph. The tailwind changed to 20 mph for the remaining 520 miles of the flight. The total time of the flight was 3 hours. Find the speed

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Question 671673: A jet flew 1200 miles with a tailwind of 50 mph. The tailwind changed to 20 mph for the remaining 520 miles of the flight. The total time of the flight was 3 hours. Find the speed of the jet relative to the ground.
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
let the speed of jet be x
first part
speed = x+50
second part speed = x+20
Time first part = 1200/(x+50)
second part time = 520/(x+20)
Time first part + time second part = 3
1200/(x+50) + 520/(x+20)=3
LCD= (x+50)(x+20)= x^2+70x+1000)
Multiply equation by the LCD
1200(x+20) +520(x+50)=3(x^2+70x+1000)
1200x+24000+520x+26000=3x^2+210x+3000
1720x+50000=3x^2+210x+3000
3x^2+210x-1720x+3000-50000=0
3x^2-1510x-47000=0
Find the roots of the equation by quadratic formula

a= 3 b= -1510 c= -47000

b^2-4ac= 2280100 - -564000
b^2-4ac= 2844100 = 1686.45

x1=( 1510 + 1686.45 )/ 6
x1= 532.74
x2=( 1510 - 1686.45 )/ 6
x2= -29.41
Ignore negative value
x = 532.74 mph the speed of plane
m.ananth@hotmail.ca