SOLUTION: With a tailwind, a plane flew the 3000 km from Calgary to Montreal in 5 h. The return flight,against the wind, took 6 h. Find the wind speed and the speed of the plane.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: With a tailwind, a plane flew the 3000 km from Calgary to Montreal in 5 h. The return flight,against the wind, took 6 h. Find the wind speed and the speed of the plane.       Log On


   

Question 343360: With a tailwind, a plane flew the 3000 km from Calgary to Montreal in 5 h. The return flight,against the wind, took 6 h. Find the wind speed and the speed of the plane.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = speed of plane in still air
Let w = wind speed
Against the wind:
3000+=+%28s+-+w%29%2A6
With the wind:
3000+=+%28s+%2B+w%29%2A5
(1) 5s+%2B+5w+=+3000
(2) 6s+-+6w+=+3000
Multiply both sides of (1) by 6 and
multiply both sides of (2) by 5
(1) 30s+%2B+30w+=+18000
(2) 30s+-+30w+=+15000
Add the equations
60s+=+33000
s+=+550 km/hr
Plug this back into (1)
(1) 5%2A550+%2B+5w+=+3000
2750+%2B+5w+=+3000
5w+=+250
w+=+50 km/hr
check:
(2) 6s+-+6w+=+3000
6%2A550+-+6%2A50+=+3000
3300+-+300+=+3000
OK