SOLUTION: 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 450miles with a tail wind.fin

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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 450miles with a tail wind.fin      Log On


   

Question 210136: 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 450miles with a tail wind.find the speed of the wind.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fspeed
Time against = Time with
350%2F%28%28160-w%29%29 = 450%2F%28%28160%2Bw%29%29
Cross multiply
350(160+w) = 450(160-w)
:
56000 + 350w = 72000 - 450w
:
350w + 450w = 72000 - 56000
:
800w = 16000
w = 16000%2F800
w = 20 mph wind
;
:
Check solution, find the time, (they should be equal):
450/180 = 2.5 hrs
350/140 = 2.5 hrs