SOLUTION: the speed of an airplane in still air is 153 mph. The plane travels 849 mph against the wind and 1402 mph with the wind in a total time of 16 hours. what is the speed?

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Question 91645: the speed of an airplane in still air is 153 mph. The plane travels 849 mph against the wind and 1402 mph with the wind in a total time of 16 hours. what is the speed?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
I ASSUME THAT YOU ARE LOOKING FOR THE SPEED OF THE WIND
Let x=speed of the wind
distance(d)=rate(r) times time(t) or d=rt; r=d/t and t=d/r
rate against the wind =153-x
amount of time the plane travels against the wind=849/(153-x)
rate with the wind=153+x
amount of time the plane travels with the wind=1402/(153+x)

Now we know that the amount of time the plane travels with the wind plus the amount of time the plane travels against the wind=16 hrs. So our equation to solve is:
1402/(153+x)+849/(153-x)=16 multiply each term by (153+x)(153-x) to get rid of fractions
1402(153-x)+849(153+x)=16(153+x)(153-x) get rid of parens
214506-1402x+129897+849x=374544-16x^2 add 16x^2 and subtract 374544 from both sides
214506-374544+16x^2-1402x+129897+849x=374544-374544+16x^2-16x^2 collect like terms
16x^2-553x-30141=0 Quadratic in standard form. Solve using the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28553+%2B-+sqrt%28+%28-553%29%5E2-4%2A16%2A%28-30141%29+%29%29%2F%282%2A16%29+
x+=+%28553+%2B-+sqrt%28+%28+2234833%29%29%2F%2832%29%29+
x+=+%28553+%2B-+1494.94%29%2F%2832%29%29+
x+=+%28553+%2B+1494.94%29%2F%2832%29%29+
x=63.998=+64 mph----------------------------speed of wind
and
x+=+%28553+-+1494.94%29%2F%2832%29%29+ discount negative value for speed of wind
CK
1402/(153+64)+849/(153-64)=16
1402/217+ 849/89=16
6.46+9.54=16
15.9993~~~~~~16 Hope this helps----ptaylor