SOLUTION: Airplane A travels 1400 km at a certain speed. Plane B travels 1000 km at a speed of 50 km/h faster than A in 3 hrs less time. Find the speed of each plane

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Airplane A travels 1400 km at a certain speed. Plane B travels 1000 km at a speed of 50 km/h faster than A in 3 hrs less time. Find the speed of each plane      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 449422: Airplane A travels 1400 km at a certain speed. Plane B travels 1000 km at a speed of 50 km/h faster than A in 3 hrs less time. Find the speed of each plane
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Plane A x mph 1400 miles
Plane B x+50 mph 1000 miles

t=d/r Time 3 hours less
1400/x=1000/(x+50)+3
1400/x-1000/(x+50)=3
LCD = x(x+50)
Multiply by LCD
1400(x+50)-1000x =3x(x+50 )
1400x+70000-1000*x=3x^2
-3X^2+250x+70000 =0
Find the roots of the equation by quadratic formula
a= -3 b= 250 c= 70000
b^2-4ac= 62500+840000
b^2-4ac= 902500
sqrt%28%09902500%09%29= 950
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=(-250 +950)/-6
x1=-116.67
x2=(-250 -950)/-6
x2=200
Ignore negative value
Plane A speed = 200 mph
Plane B speed = 250 mph