Hello,
An airplane makes a 990 km flight with a tailwind & returns, flying into the same wind. The total flying time is 3 hrs 20 mins & the airplanes speed in still air is 600 km/hr what is the the speed of the wind?
I'm as far as (990/(600-x))+(990/600+x))=10/3
but I can't figure out how to go from there!
Thanks a bunch :)
Kayla
same distance, there and back
v1*t1=v2*t2=990km
t1=3 1/3 hr -t2
v1=600+w
v2=600-w
(600+w)t1=990 or
t1=990/(600+w)
10/3-t1=990/(600-w)
10/3-990/(600+w) = 990/(600-w) so your equation is correct.
now, multipy each side by (600-w)(600+w)/990
10(600^2-w^2)/(3*990) = 600+w+600-w)
check that. Now is simplifies considerably, gather terms, and you have a quadratic equation. use the quadratic formula.
multiply by the LCD
[990 (600 + x)] + [990 (600 - x)] = 10/3 (600 - x)(600 + x)
1188000 = 10/3 (360000 - x^2) ... 356400 = 360000 - x^2
x^2 = 3600
To solve the equation (990/(600-x))+(990/(600+x))=(10/3), you can start by simplifying the equation by finding a common denominator for the fractions on the left side:
Multiply the first term by (600+x) and the second term by (600-x):
(990)(600+x)+(990)(600-x)=(10/3)(600^2-(x^2))
Now, distribute and simplify:
(990)(600)+(990)(x)+(990)(600)-(990)(x)=(10/3)(360,000-x^2)
Combine like terms:
(990)(600)+(990)(600)=(10/3)(360,000-x^2)
2(990)(600)=(10/3)(360,000-x^2)
Simplify both sides of the equation:
1188,000 = (3/10)(360,000-x^2)
Multiply both sides of the equation by (10/3):
(10/3)(1188,000) = 360,000-x^2
Simplify:
3,960,000 = 360,000-x^2
Rearrange the equation:
x^2 = 360,000 - 3,960,000
Simplify:
x^2 = -3,600,000
Take the square root of both sides:
x = ±√(-3,600,000)
Since the square root of a negative number is not defined in the real number system, it means that there is no real solution to this equation.
Therefore, there is no solution for the speed of the wind in this case.
Hi Kayla! I can help you with that. You are on the right track with the equation you have set up:
(990/(600-x)) + (990/(600+x)) = 10/3
To solve this equation, we can start by getting rid of the denominators. We can do this by finding a common denominator, which in this case is (600 - x)(600 + x):
[(990)(600 + x)] + [(990)(600 - x)] = (10/3)[(600 - x)(600 + x)]
Next, we can simplify the equation by distributing and combining like terms:
(990)(600 + x) + (990)(600 - x) = (10/3)(360000 - x^2)
Now, we can simplify the equation further:
594000 + 990x + 594000 - 990x = 1200000 - (10/3)x^2
Simplifying the equation, we get:
1188000 = 1200000 - (10/3)x^2
Rearranging the equation, we get a quadratic equation:
(10/3)x^2 = 1200000 - 1188000
(10/3)x^2 = 12000
To solve for x, we can multiply both sides by 3/10 to isolate x:
x^2 = (12000)(3/10)
x^2 = 3600
Taking the square root of both sides, we get:
x = ±60
Since the speed of the wind cannot be negative, we can discard the negative value. Therefore, the speed of the wind is 60 km/hr.
I hope this helps! Let me know if you have any other questions.