Question 620145
Let s = the plane's airspeed
The total time of the trip is 30 mins = 1/2 hr; the speed of the wind = 30 km/hr
Since t = d/v, we can write the following for the total time of the trip:
150/(s+30) + 65/(s-30) = 0.5
Combine fractions using the common denominator, and cross-multiply:
150(s-30) + 65(s+30) = 0.5(s^2-900)
Simplify and collect terms:
s^2 - 430s + 4200 = 0
This can be factored as
(s-10)(s-420) = 0
The solutions are s = 10, s = 420
Since the speed of the plane cannot be less than the wind speed, we take the 2nd solution.
So s = 420 km/hr
Check:
150/450 + 65/390 = 1/3 + 1/6 = 3/6 = 1/2