Question 414498
A plane flies 720 miles against the wind in 3 hours.
 The return trip with the wind takes only 2 1/2 hours.
 Find the speed of the wind.
 Find the speed of the plane in still air
:
Let s = speed of the plane in still air
Let w = speed of the wind
:
Then we can say
(s+w) = effective speed with the wind
and
(s-w) = effective speed against the wind
:
Write a distance equation for each trip; dist = time * speed
2.5(s+w) = 720
and
3(s-w) = 720
:
We can simplify this and use elimination to solve this
divide the 1st equation by 2.5
s + w = {{{720/2.5}}}
s + w = 288
and
divide the 2nd equation by 3
s - w = {{{720/3}}}
s - w = 240
:
Add these two equations.
s - w = 240
s + w = 288
----------------addition eliminates w, find s
2s = 528
s = {{{528/2}}}
s = 264 mph is the plane speed in still air
:
Find w using the equation: s + w = 288
264 + w = 288
w = 288 - 264
w = 24 mph is the wind speed
:
Check solutions in the 2nd original equation: 3(s-w) = 720
3(264 - 24) =
3 * 240 = 720 mi confirms our solutions of s = 264, w = 24