<PRE><B>Question 139664</B>
In the time it takes to fly 360 miles with a head wind, she can only fly 240 mies against the headwind. if the speed of the plane in still air is 150 mph, find the wind speed.
:
Let x = the wind speed
then
(150-x) = ground speed against the wind
and
(150+x) = ground speed with the wind
:
write a time equation: Time = dist/speed
:
With time = Against time
{{{360/((150+x))}}} = {{{240/((150-x))}}}
Cross multiply
240(150+x) = 360(150-x)
;
36000 + 240x = 54000 - 360x
:
240x + 360x = 54000 - 36000
:
600x = 18000
x = {{{18000/600}}}
x = 30 mph is the wind speed
:
:
Check solution in original equation: Against speed = 120, With speed = 180
{{{360/180}}} = {{{240/120}}}; confirms our solution</PRE>