SOLUTION: Speed of an airplane in still air is 255 km/h. plane travels 675km against wind and 1449 km with the wind in a total of 10 hr. What is the speed of the wind?

Question 78762: Speed of an airplane in still air is 255 km/h. plane travels 675km against wind and 1449 km with the wind in a total of 10 hr. What is the speed of the wind?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Speed of an airplane in still air is 255 km/h. Plane travels 675 km against wind and 1449 km with the wind in a total of 10 hr. What is the speed of the wind?
:
Let x = speed of the wind
:
Speed with the wind = (255+x)
Speed against the wind = (255-x)
:
Time = dist/speed
:
Time against the wind + Time with the wind = 10 hrs
+ = 10
:
Multiply equation by (255-x)(255+x) and you have:
675(255+x) + 1449(255-x) = 10(255+x)(255-x)
:
172125 + 675x + 369495 - 1449x = 10(65025 - x^2)
:
541620 - 774x = 650250 - 10x^2
:
10x^2 - 774x + 541620 - 650250 = 0; all terms on the left
:
10x^2 - 774x - 108630 = 0: a quadratic equation
:
Simplify, divide equation by 2:
5x^2 - 387x - 54315 = 0
:
Use the quadratic formula: a=5, b=-387, c=-54315
:
The positive solution: x = 149.47, call it 149.5 mph is the wind speed
:
Check on a calculator the times with and against the wind:
675/(255-149.5) = 6.4 hrs
1489/(255+149.5)= 3.7 hrs
-------------------------
Total times = 10.1 ~ 10 hrs as given
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