<PRE><B>Question 210136</B>
a plane flies with a ground speed of 160 miles per hour if there is no wind.
 it travels 350 miles with a head wind and in the same time it takes to go 450
 miles with a tail wind. 
find the speed of the wind.
:
Let w = wind speed
then
(160+w) = speed with the wind
and
(160-w) = speed against the wind
:
They fly the two distances in equal times. Write a time equation; Time = {{{dist/speed}}}
Time against = Time with
{{{350/((160-w))}}} = {{{450/((160+w))}}}
Cross multiply
350(160+w) = 450(160-w)
:
56000 + 350w = 72000 - 450w
:
350w + 450w = 72000 - 56000
:
800w = 16000
w = {{{16000/800}}}
w = 20 mph wind
;
:
Check solution, find the time, (they should be equal):
450/180 = 2.5 hrs
350/140 = 2.5 hrs


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