SOLUTION: The speed of an airplane in still air is 250 km. The plane travels 632 km against the wind and 1343 km with the wind in a total time of 15 hours. What is the speed of the wind?

Question 152709: The speed of an airplane in still air is 250 km. The plane travels 632 km
against the wind and 1343 km with the wind in a total time of 15 hours. What is the speed of the wind?
Thank You. I have been at this problem for hours.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The speed of an airplane in still air is 250 km. The plane travels 632 km
against the wind and 1343 km with the wind in a total time of 15 hours. What is the speed of the wind?
:
Write down what you know:
Let x = speed of the wind
then
(250+x) = the speed of the plane with the wind
and
(250-x) = the speed against the wind
:
Write a time equation: Time = Dist/speed
:
Time with + time against = 15 hrs
+ = 15
;
Multiply equation by the common denominator: (250+x)(250-x), results
1343(250-x) + 632(250+x) = 15(250+x)(250-x)
:
335750 - 1343x + 158000 + 632x = 15(62500 - x^2); FOILed
:
493750 - 711x = 937500 - 15x^2
Arrange as a quadratic equation
15x^2 - 711x + 493750 - 937500 = 0
:
15x^2 - 711x - 443750 = 0
:
A nasty equation to be solved by the quadratic formula

In this problem a=15; b=-711; c= -443750

The positive solution

x = 197.3 is the speed of the wind
:
:
Check this rather extreme solution by finding the total time:
Speed with = 447.3; against = 52.7
Using a calc
1343/447.3 + 632/52.7 =
3.00 + 11.99 = 14.99 ~ 15 hrs

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