Question 115726
s = the plane's speed in still air
w = wind speed
The problem says {{{w = 30}}} mi/hr
(time going) + (time returning) = total time
The problems says total time = 10 hrs
Note that distance/rate = time
{{{720 / (s - w) + 720 / (s + w) = 10}}}
{{{720 / (s - 30) + 720 / (s + 30) = 10}}}
multiply both sides by {{{(s - 30)(s + 30)}}}
{{{720(s + 30) + 720(s - 30) = 10(s + 30)(s - 30)}}}
{{{720s + 21600 + 720s - 21600 = 10(s^2 - 900)}}}
{{{1440s = 10s^2 - 9000}}}
{{{10s^2 - 1440s - 9000 = 0}}}
{{{s^2 - 144s - 900 = 0}}}
solve using quadratic formula
{{{s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a = 1
b = -144
c = -900
{{{s = (-(-144) +- sqrt( (-144)^2-4*1*(-900) ))/(2*1) }}}
{{{s = (144 +- sqrt(20736 + 3600)) / 2}}}
{{{s = (144 +- 156) / 2}}}
{{{s = 150}}}
{{{s = -6}}}
The positive answer is the only one that makes sense
The plane's speed in still air is 150 mi/hr
check answer:
{{{720 / (s - w) + 720 / (s + w) = 10}}}
{{{720 / (150 - 30) + 720 / (150 + 30) = 10}}}
{{{720 / 120 + 720 / 180 = 10}}}
{{{6 + 4 = 10}}}
OK