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

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) (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 = 2236 1/9

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

RELATED QUESTIONS
a jet plane traveling at a constant goes 1200 mi with the wind , then turns around and (answered by mananth)

I need some help in trying to solve the following equation. I have been trying to solve... (answered by ankor@dixie-net.com)

a jet plane traveling at a constant speed goes 1200 miles with the wind, then turns... (answered by lwsshak3)

a jet plane travelling at a constant speed goes 1200 mi with the wind , then turns around (answered by ankor@dixie-net.com)

A bicycle traveling at a constant speed goes 45 miles with the wind turns around and... (answered by dabanfield,palanisamy)

a boat traveling at a constant speed goes 45 miles with the current, then turns around... (answered by Edwin McCravy)

A plane travels a distance of 1000 km in 2.5 hours while flying against the wind and in 2 (answered by rwm)

The speed of an airplane in still air is 250 km. The plane travels 632 km against the... (answered by ankor@dixie-net.com)

A plane travels 300 miles against the wind in five hours, then turns and travels 330... (answered by mananth)