SOLUTION: With a certain tail wind a jet air craft arrives at its destination 1,890 miles away in 3 hours. Flying against the same wind, the plane makes the return trip in 3 3/8 hours. Find

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Question 151830: With a certain tail wind a jet air craft arrives at its destination 1,890 miles away in 3 hours. Flying against the same wind, the plane makes the return trip in 3 3/8 hours. Find the windspeed and airspeed.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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With a certain tail wind a jet air craft arrives at its destination 1,890 miles away in 3 hours. Flying against the same wind, the plane makes the return trip in 3 3/8 hours. Find the windspeed and airspeed.
:
Let x = airspeed
Let y = windspeed
then
(x+y) = speed with the wind
(x-y) = speed against the wind
:
Write distance equations for each trip: Dist = time * speed
:
3(x+y) = 1890
Simplify, divide equation by 3
x + y = 1890/3
x + y = 630
y = (630-x)
and
33%2F8(x - y) = 1890
27%2F8(x - y) = 1890
Multiply eq by 8 to get rid of the denominator
27(x - y) = 8*1890
27x - 27y = 15120
Substitute (630-x) for y:
27x - 27(630-x) = 15120
27x - 17010 + 27x = 15120
27x + 27x = 15120 + 17010
54x = 32130
x = 32130%2F54
x = 595 mph plane airspeed
:
Use equation: x + y = 630 to find y
595 + y = 630
y = 630-595
y = 35 mph is the windspeed
:
:
Check solution in equation: 27%2F8(x - y) = 1890:
27%2F8(595 - 35) = 1890
27%2F8(560) = 1890
Using a calc:
1890 = 1890