Question 759611
An airplane flies 594 miles with a 30-mph tailwind and then flies back into the 30-mph wind. If the time for the round trip was four hours, find the speed of the airplane in calm air.
let x=speed of airplane in calm air
x+30= speed of airplane with tail wind
x-30= speed of airplane with downwind
travel time=distance/speed
..
{{{594/(x-30)+594/x=4}}}
LCD:x(x-30)
{{{594x+594(x-30)=4x(x-30)}}}
{{{594x+594x-17820=4x^2-120x)}}}
4x^2-1308x+17820=0
x^2-327x+4455=0
solve for x by quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1, b=-327, c=4455
x≈14.24 (reject)
or
x≈312.76
speed of airplane in calm air≈312.76 mph