SOLUTION: a jet plane traveling at a constant speed goes 1200 km with the wind, then turns around and travels for 1000 km against the wind. If the speed of the wind is 50 km/h and the total

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Question 914753: a jet plane traveling at a constant speed goes 1200 km with the wind, then turns around and travels for 1000 km against the wind. If the speed of the wind is 50 km/h and the total flight took 4 hours, find the speed of the plane.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Plane speed x mph
wind speed 50 mph

Distance with wind 1200 miles
Distance against wind 1000 miles

spee with wind x + 50 mph
speed against x 50 mph
Total time = 4 hours
Time with current= 1200 /( x + 50 )
time against current 1000 / ( x -50 )

Time with current + time against = 4 hours

1200 /( x + 50 ) + 1000 /(x -50 ) = 4
LCD = ( x + 50 )* (x -50 )
multiply the equation by the LCD
we get
1200 * (x -50 )+ 1000 (x + 50 )= 4 (x^2- 2500 )
1200 x -60000 + 1000 x + 50000 )= 4 X^2 10000
2200 x 0 = 10 X^2 -10000
4 X^2 -2200 x 0 + -10000 = 0
4 X^2+ -2200 x+ -10000 = 0
/ 1
4 X^2 -2200 x -10000 = 0

Find the roots of the equation by quadratic formula

a= 4 b= -2200 c= -10000

b^2-4ac= 4840000 - -160000
b^2-4ac= 5000000 sqrt%28%095000000++++%09%29= 2236 1/9
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 2200 + 2236 1/9 )/ 8
x1= 554 1/2
x2=( 2200 -2236 1/9 ) / 8
x2= -4 1/2
Ignore negative value mph
x = 554 1/2